4x(3x+6)=-9

Solution for 4x(3x+6)=-9 equation:

Simplifying
4x(3x + 6) = -9

Reorder the terms:
4x(6 + 3x) = -9
(6 * 4x + 3x * 4x) = -9
(24x + 12x2) = -9

Solving
24x + 12x2 = -9

Solving for variable 'x'.

Reorder the terms:
9 + 24x + 12x2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + 24x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 8x + 4x2) = 0

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

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 0

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

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

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1.5, -0.5}