-2x(3x-6)+18=24

Solution for -2x(3x-6)+18=24 equation:

Simplifying
-2x(3x + -6) + 18 = 24

Reorder the terms:
-2x(-6 + 3x) + 18 = 24
(-6 * -2x + 3x * -2x) + 18 = 24
(12x + -6x2) + 18 = 24

Reorder the terms:
18 + 12x + -6x2 = 24

Solving
18 + 12x + -6x2 = 24

Solving for variable 'x'.

Reorder the terms:
18 + -24 + 12x + -6x2 = 24 + -24

Combine like terms: 18 + -24 = -6
-6 + 12x + -6x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-6 + 12x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 2x + -1x2) = 0

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

Ignore the factor 6.
Subproblem 1
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
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 = {1, 1}