66=2x^2-20x+108

Solution for 66=2x^2-20x+108 equation:

Simplifying
66 = 2x2 + -20x + 108

Reorder the terms:
66 = 108 + -20x + 2x2

Solving
66 = 108 + -20x + 2x2

Solving for variable 'x'.

Combine like terms: 66 + -108 = -42
-42 + 20x + -2x2 = 108 + -20x + 2x2 + -108 + 20x + -2x2

Reorder the terms:
-42 + 20x + -2x2 = 108 + -108 + -20x + 20x + 2x2 + -2x2

Combine like terms: 108 + -108 = 0
-42 + 20x + -2x2 = 0 + -20x + 20x + 2x2 + -2x2
-42 + 20x + -2x2 = -20x + 20x + 2x2 + -2x2

Combine like terms: -20x + 20x = 0
-42 + 20x + -2x2 = 0 + 2x2 + -2x2
-42 + 20x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-42 + 20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + 10x + -1x2) = 0

Factor a trinomial.
2((-7 + x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
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 = {7, 3}