x^2=18x-32

Solution for x^2=18x-32 equation:

Simplifying
x2 = 18x + -32

Reorder the terms:
x2 = -32 + 18x

Solving
x2 = -32 + 18x

Solving for variable 'x'.

Reorder the terms:
32 + -18x + x2 = -32 + 18x + 32 + -18x

Reorder the terms:
32 + -18x + x2 = -32 + 32 + 18x + -18x

Combine like terms: -32 + 32 = 0
32 + -18x + x2 = 0 + 18x + -18x
32 + -18x + x2 = 18x + -18x

Combine like terms: 18x + -18x = 0
32 + -18x + x2 = 0

Factor a trinomial.
(2 + -1x)(16 + -1x) = 0

Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(16 + -1x)' equal to zero and attempt to solve:

Simplifying
16 + -1x = 0

Solving
16 + -1x = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1x = 0 + -16
-1x = 0 + -16

Combine like terms: 0 + -16 = -16
-1x = -16

Divide each side by '-1'.
x = 16

Simplifying
x = 16
Solution
x = {2, 16}