2x^2-18x=72

Solution for 2x^2-18x=72 equation:

Simplifying
2x2 + -18x = 72

Reorder the terms:
-18x + 2x2 = 72

Solving
-18x + 2x2 = 72

Solving for variable 'x'.

Reorder the terms:
-72 + -18x + 2x2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + -9x + x2) = 0

Factor a trinomial.
2((-3 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-3, 12}