2x^2=18x-36

Solution for 2x^2=18x-36 equation:

Simplifying
2x2 = 18x + -36

Reorder the terms:
2x2 = -36 + 18x

Solving
2x2 = -36 + 18x

Solving for variable 'x'.

Reorder the terms:
36 + -18x + 2x2 = -36 + 18x + 36 + -18x

Reorder the terms:
36 + -18x + 2x2 = -36 + 36 + 18x + -18x

Combine like terms: -36 + 36 = 0
36 + -18x + 2x2 = 0 + 18x + -18x
36 + -18x + 2x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
36 + -18x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(18 + -9x + 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}