3(x+1)=6x(x-2)-6

Solution for 3(x+1)=6x(x-2)-6 equation:

Simplifying
3(x + 1) = 6x(x + -2) + -6

Reorder the terms:
3(1 + x) = 6x(x + -2) + -6
(1 * 3 + x * 3) = 6x(x + -2) + -6
(3 + 3x) = 6x(x + -2) + -6

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

Reorder the terms:
3 + 3x = -6 + -12x + 6x2

Solving
3 + 3x = -6 + -12x + 6x2

Solving for variable 'x'.

Reorder the terms:
3 + 6 + 3x + 12x + -6x2 = -6 + -12x + 6x2 + 6 + 12x + -6x2

Combine like terms: 3 + 6 = 9
9 + 3x + 12x + -6x2 = -6 + -12x + 6x2 + 6 + 12x + -6x2

Combine like terms: 3x + 12x = 15x
9 + 15x + -6x2 = -6 + -12x + 6x2 + 6 + 12x + -6x2

Reorder the terms:
9 + 15x + -6x2 = -6 + 6 + -12x + 12x + 6x2 + -6x2

Combine like terms: -6 + 6 = 0
9 + 15x + -6x2 = 0 + -12x + 12x + 6x2 + -6x2
9 + 15x + -6x2 = -12x + 12x + 6x2 + -6x2

Combine like terms: -12x + 12x = 0
9 + 15x + -6x2 = 0 + 6x2 + -6x2
9 + 15x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
9 + 15x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 5x + -2x2) = 0

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

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
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 = {3, -0.5}