5x^2-18x+18=x^2

Solution for 5x^2-18x+18=x^2 equation:

Simplifying
5x2 + -18x + 18 = x2

Reorder the terms:
18 + -18x + 5x2 = x2

Solving
18 + -18x + 5x2 = x2

Solving for variable 'x'.

Combine like terms: 5x2 + -1x2 = 4x2
18 + -18x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
18 + -18x + 4x2 = 0

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
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
Solution
x = {1.5, 3}