6(x+2)=-18x+6(x^2-3)

Solution for 6(x+2)=-18x+6(x^2-3) equation:

Simplifying
6(x + 2) = -18x + 6(x2 + -3)

Reorder the terms:
6(2 + x) = -18x + 6(x2 + -3)
(2 * 6 + x * 6) = -18x + 6(x2 + -3)
(12 + 6x) = -18x + 6(x2 + -3)

Reorder the terms:
12 + 6x = -18x + 6(-3 + x2)
12 + 6x = -18x + (-3 * 6 + x2 * 6)
12 + 6x = -18x + (-18 + 6x2)

Reorder the terms:
12 + 6x = -18 + -18x + 6x2

Solving
12 + 6x = -18 + -18x + 6x2

Solving for variable 'x'.

Reorder the terms:
12 + 18 + 6x + 18x + -6x2 = -18 + -18x + 6x2 + 18 + 18x + -6x2

Combine like terms: 12 + 18 = 30
30 + 6x + 18x + -6x2 = -18 + -18x + 6x2 + 18 + 18x + -6x2

Combine like terms: 6x + 18x = 24x
30 + 24x + -6x2 = -18 + -18x + 6x2 + 18 + 18x + -6x2

Reorder the terms:
30 + 24x + -6x2 = -18 + 18 + -18x + 18x + 6x2 + -6x2

Combine like terms: -18 + 18 = 0
30 + 24x + -6x2 = 0 + -18x + 18x + 6x2 + -6x2
30 + 24x + -6x2 = -18x + 18x + 6x2 + -6x2

Combine like terms: -18x + 18x = 0
30 + 24x + -6x2 = 0 + 6x2 + -6x2
30 + 24x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
30 + 24x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + 4x + -1x2) = 0

Factor a trinomial.
6((5 + -1x)(1 + x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {5, -1}