Solve for t 0=-16t^2+48t+28

Math
0=-16t2+48t+28
Rewrite the equation as -16t2+48t+28=0.
-16t2+48t+28=0
Factor the left side of the equation.
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Factor -4 out of -16t2+48t+28.
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Factor -4 out of -16t2.
-4(4t2)+48t+28=0
Factor -4 out of 48t.
-4(4t2)-4(-12t)+28=0
Factor -4 out of 28.
-4(4t2)-4(-12t)-4⋅-7=0
Factor -4 out of -4(4t2)-4(-12t).
-4(4t2-12t)-4⋅-7=0
Factor -4 out of -4(4t2-12t)-4(-7).
-4(4t2-12t-7)=0
-4(4t2-12t-7)=0
Factor.
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Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-7=-28 and whose sum is b=-12.
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Factor -12 out of -12t.
-4(4t2-12t-7)=0
Rewrite -12 as 2 plus -14
-4(4t2+(2-14)t-7)=0
Apply the distributive property.
-4(4t2+2t-14t-7)=0
-4(4t2+2t-14t-7)=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
-4((4t2+2t)-14t-7)=0
Factor out the greatest common factor (GCF) from each group.
-4(2t(2t+1)-7(2t+1))=0
-4(2t(2t+1)-7(2t+1))=0
Factor the polynomial by factoring out the greatest common factor, 2t+1.
-4((2t+1)(2t-7))=0
-4((2t+1)(2t-7))=0
Remove unnecessary parentheses.
-4(2t+1)(2t-7)=0
-4(2t+1)(2t-7)=0
-4(2t+1)(2t-7)=0
Divide each term by -4 and simplify.
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Divide each term in -4(2t+1)(2t-7)=0 by -4.
-4(2t+1)(2t-7)-4=0-4
Simplify -4(2t+1)(2t-7)-4.
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Cancel the common factor of -4.
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Cancel the common factor.
-4(2t+1)(2t-7)-4=0-4
Divide (2t+1)(2t-7) by 1.
(2t+1)(2t-7)=0-4
(2t+1)(2t-7)=0-4
Expand (2t+1)(2t-7) using the FOIL Method.
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Apply the distributive property.
2t(2t-7)+1(2t-7)=0-4
Apply the distributive property.
2t(2t)+2t⋅-7+1(2t-7)=0-4
Apply the distributive property.
2t(2t)+2t⋅-7+1(2t)+1⋅-7=0-4
2t(2t)+2t⋅-7+1(2t)+1⋅-7=0-4
Simplify and combine like terms.
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Simplify each term.
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Multiply t by t.
2⋅2t2+2t⋅-7+1(2t)+1⋅-7=0-4
Multiply 2 by 2.
4t2+2t⋅-7+1(2t)+1⋅-7=0-4
Multiply -7 by 2.
4t2-14t+1(2t)+1⋅-7=0-4
Multiply 2t by 1.
4t2-14t+2t+1⋅-7=0-4
Multiply -7 by 1.
4t2-14t+2t-7=0-4
4t2-14t+2t-7=0-4
Add -14t and 2t.
4t2-12t-7=0-4
4t2-12t-7=0-4
4t2-12t-7=0-4
Divide 0 by -4.
4t2-12t-7=0
4t2-12t-7=0
Factor by grouping.
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For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅-7=-28 and whose sum is b=-12.
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Factor -12 out of -12t.
4t2-12t-7=0
Rewrite -12 as 2 plus -14
4t2+(2-14)t-7=0
Apply the distributive property.
4t2+2t-14t-7=0
4t2+2t-14t-7=0
Factor out the greatest common factor from each group.
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Group the first two terms and the last two terms.
(4t2+2t)-14t-7=0
Factor out the greatest common factor (GCF) from each group.
2t(2t+1)-7(2t+1)=0
2t(2t+1)-7(2t+1)=0
Factor the polynomial by factoring out the greatest common factor, 2t+1.
(2t+1)(2t-7)=0
(2t+1)(2t-7)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
2t+1=0
2t-7=0
Set the first factor equal to 0 and solve.
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Set the first factor equal to 0.
2t+1=0
Subtract 1 from both sides of the equation.
2t=-1
Divide each term by 2 and simplify.
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Divide each term in 2t=-1 by 2.
2t2=-12
Cancel the common factor of 2.
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Cancel the common factor.
2t2=-12
Divide t by 1.
t=-12
t=-12
Move the negative in front of the fraction.
t=-12
t=-12
t=-12
Set the next factor equal to 0 and solve.
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Set the next factor equal to 0.
2t-7=0
Add 7 to both sides of the equation.
2t=7
Divide each term by 2 and simplify.
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Divide each term in 2t=7 by 2.
2t2=72
Cancel the common factor of 2.
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Cancel the common factor.
2t2=72
Divide t by 1.
t=72
t=72
t=72
t=72
The final solution is all the values that make (2t+1)(2t-7)=0 true.
t=-12,72
The result can be shown in multiple forms.
Exact Form:
t=-12,72
Decimal Form:
t=-0.5,3.5
Mixed Number Form:
t=-12,312
Solve for t 0=-16t^2+48t+28

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