-4(3a+1)=9a^2

Solution for -4(3a+1)=9a^2 equation:

Simplifying
-4(3a + 1) = 9a2

Reorder the terms:
-4(1 + 3a) = 9a2
(1 * -4 + 3a * -4) = 9a2
(-4 + -12a) = 9a2

Solving
-4 + -12a = 9a2

Solving for variable 'a'.

Combine like terms: 9a2 + -9a2 = 0
-4 + -12a + -9a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 12a + 9a2) = 0

Factor a trinomial.
-1((2 + 3a)(2 + 3a)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(2 + 3a)' equal to zero and attempt to solve:

Simplifying
2 + 3a = 0

Solving
2 + 3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a = 0 + -2
3a = 0 + -2

Combine like terms: 0 + -2 = -2
3a = -2

Divide each side by '3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Subproblem 2
Set the factor '(2 + 3a)' equal to zero and attempt to solve:

Simplifying
2 + 3a = 0

Solving
2 + 3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 3a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3a = 0 + -2
3a = 0 + -2

Combine like terms: 0 + -2 = -2
3a = -2

Divide each side by '3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Solution
a = {-0.6666666667, -0.6666666667}