3a2+4a=4

Move 4 to the left side of the equation by subtracting it from both sides.

3a2+4a-4=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=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.

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.

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