2x^2-36x+162=32

Solution for 2x^2-36x+162=32 equation:

Simplifying
2x2 + -36x + 162 = 32

Reorder the terms:
162 + -36x + 2x2 = 32

Solving
162 + -36x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
162 + -32 + -36x + 2x2 = 32 + -32

Combine like terms: 162 + -32 = 130
130 + -36x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
130 + -36x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(65 + -18x + x2) = 0

Factor a trinomial.
2((5 + -1x)(13 + -1x)) = 0

Ignore the factor 2.
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 '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {5, 13}