0=-16t2+48t+28

Rewrite the equation as -16t2+48t+28=0.

-16t2+48t+28=0

Factor -4 out of -16t2+48t+28.

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.

Factor by grouping.

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.

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.

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 in -4(2t+1)(2t-7)=0 by -4.

-4(2t+1)(2t-7)-4=0-4

Simplify -4(2t+1)(2t-7)-4.

Cancel the common factor of -4.

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.

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.

Simplify each term.

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

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.

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.

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.

2t+1=0

Subtract 1 from both sides of the equation.

2t=-1

Divide each term by 2 and simplify.

Divide each term in 2t=-1 by 2.

2t2=-12

Cancel the common factor of 2.

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.

2t-7=0

Add 7 to both sides of the equation.

2t=7

Divide each term by 2 and simplify.

Divide each term in 2t=7 by 2.

2t2=72

Cancel the common factor of 2.

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