# Solve for a 3a^2+4a=4 3a2+4a=4
Move 4 to the left side of the equation by subtracting it from both sides.
3a2+4a-4=0
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=3⋅-4=-12 and whose sum is b=4.
Factor 4 out of 4a.
3a2+4(a)-4=0
Rewrite 4 as -2 plus 6
3a2+(-2+6)a-4=0
Apply the distributive property.
3a2-2a+6a-4=0
3a2-2a+6a-4=0
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(3a2-2a)+6a-4=0
Factor out the greatest common factor (GCF) from each group.
a(3a-2)+2(3a-2)=0
a(3a-2)+2(3a-2)=0
Factor the polynomial by factoring out the greatest common factor, 3a-2.
(3a-2)(a+2)=0
(3a-2)(a+2)=0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
3a-2=0
a+2=0
Set the first factor equal to 0 and solve.
Set the first factor equal to 0.
3a-2=0
Add 2 to both sides of the equation.
3a=2
Divide each term by 3 and simplify.
Divide each term in 3a=2 by 3.
3a3=23
Cancel the common factor of 3.
Cancel the common factor.
3a3=23
Divide a by 1.
a=23
a=23
a=23
a=23
Set the next factor equal to 0 and solve.
Set the next factor equal to 0.
a+2=0
Subtract 2 from both sides of the equation.
a=-2
a=-2
The final solution is all the values that make (3a-2)(a+2)=0 true.
a=23,-2
The result can be shown in multiple forms.
Exact Form:
a=23,-2
Decimal Form:
a=0.6‾,-2
Solve for a 3a^2+4a=4

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