x(2x-6)=36

Solution for x(2x-6)=36 equation:

Simplifying
x(2x + -6) = 36

Reorder the terms:
x(-6 + 2x) = 36
(-6 * x + 2x * x) = 36
(-6x + 2x2) = 36

Solving
-6x + 2x2 = 36

Solving for variable 'x'.

Reorder the terms:
-36 + -6x + 2x2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -3x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(6 + -1x)) = 0

Ignore the factor 2.
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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-3, 6}