4x(3x+2)=-9x-6

Solution for 4x(3x+2)=-9x-6 equation:

Simplifying
4x(3x + 2) = -9x + -6

Reorder the terms:
4x(2 + 3x) = -9x + -6
(2 * 4x + 3x * 4x) = -9x + -6
(8x + 12x2) = -9x + -6

Reorder the terms:
8x + 12x2 = -6 + -9x

Solving
8x + 12x2 = -6 + -9x

Solving for variable 'x'.

Reorder the terms:
6 + 8x + 9x + 12x2 = -6 + -9x + 6 + 9x

Combine like terms: 8x + 9x = 17x
6 + 17x + 12x2 = -6 + -9x + 6 + 9x

Reorder the terms:
6 + 17x + 12x2 = -6 + 6 + -9x + 9x

Combine like terms: -6 + 6 = 0
6 + 17x + 12x2 = 0 + -9x + 9x
6 + 17x + 12x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
6 + 17x + 12x2 = 0

Factor a trinomial.
(3 + 4x)(2 + 3x) = 0

Subproblem 1
Set the factor '(3 + 4x)' equal to zero and attempt to solve:

Simplifying
3 + 4x = 0

Solving
3 + 4x = 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 + 4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x = 0 + -3
4x = 0 + -3

Combine like terms: 0 + -3 = -3
4x = -3

Divide each side by '4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

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

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

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

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

Simplifying
x = -0.6666666667
Solution
x = {-0.75, -0.6666666667}