72=2x^2-12x+82

Solution for 72=2x^2-12x+82 equation:

Simplifying
72 = 2x2 + -12x + 82

Reorder the terms:
72 = 82 + -12x + 2x2

Solving
72 = 82 + -12x + 2x2

Solving for variable 'x'.

Combine like terms: 72 + -82 = -10
-10 + 12x + -2x2 = 82 + -12x + 2x2 + -82 + 12x + -2x2

Reorder the terms:
-10 + 12x + -2x2 = 82 + -82 + -12x + 12x + 2x2 + -2x2

Combine like terms: 82 + -82 = 0
-10 + 12x + -2x2 = 0 + -12x + 12x + 2x2 + -2x2
-10 + 12x + -2x2 = -12x + 12x + 2x2 + -2x2

Combine like terms: -12x + 12x = 0
-10 + 12x + -2x2 = 0 + 2x2 + -2x2
-10 + 12x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-10 + 12x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6x + -1x2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {5, 1}