-3x(2x-6)=4(-2x+2)+2x+10

Solution for -3x(2x-6)=4(-2x+2)+2x+10 equation:

Simplifying
-3x(2x + -6) = 4(-2x + 2) + 2x + 10

Reorder the terms:
-3x(-6 + 2x) = 4(-2x + 2) + 2x + 10
(-6 * -3x + 2x * -3x) = 4(-2x + 2) + 2x + 10
(18x + -6x2) = 4(-2x + 2) + 2x + 10

Reorder the terms:
18x + -6x2 = 4(2 + -2x) + 2x + 10
18x + -6x2 = (2 * 4 + -2x * 4) + 2x + 10
18x + -6x2 = (8 + -8x) + 2x + 10

Reorder the terms:
18x + -6x2 = 8 + 10 + -8x + 2x

Combine like terms: 8 + 10 = 18
18x + -6x2 = 18 + -8x + 2x

Combine like terms: -8x + 2x = -6x
18x + -6x2 = 18 + -6x

Solving
18x + -6x2 = 18 + -6x

Solving for variable 'x'.

Reorder the terms:
-18 + 18x + 6x + -6x2 = 18 + -6x + -18 + 6x

Combine like terms: 18x + 6x = 24x
-18 + 24x + -6x2 = 18 + -6x + -18 + 6x

Reorder the terms:
-18 + 24x + -6x2 = 18 + -18 + -6x + 6x

Combine like terms: 18 + -18 = 0
-18 + 24x + -6x2 = 0 + -6x + 6x
-18 + 24x + -6x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-18 + 24x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 4x + -1x2) = 0

Factor a trinomial.
6((-3 + x)(1 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

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

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

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

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {3, 1}