12x(x+2)=7x-6

Solution for 12x(x+2)=7x-6 equation:

Simplifying
12x(x + 2) = 7x + -6

Reorder the terms:
12x(2 + x) = 7x + -6
(2 * 12x + x * 12x) = 7x + -6
(24x + 12x2) = 7x + -6

Reorder the terms:
24x + 12x2 = -6 + 7x

Solving
24x + 12x2 = -6 + 7x

Solving for variable 'x'.

Reorder the terms:
6 + 24x + -7x + 12x2 = -6 + 7x + 6 + -7x

Combine like terms: 24x + -7x = 17x
6 + 17x + 12x2 = -6 + 7x + 6 + -7x

Reorder the terms:
6 + 17x + 12x2 = -6 + 6 + 7x + -7x

Combine like terms: -6 + 6 = 0
6 + 17x + 12x2 = 0 + 7x + -7x
6 + 17x + 12x2 = 7x + -7x

Combine like terms: 7x + -7x = 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}