2x^2-24x+146=82

Solution for 2x^2-24x+146=82 equation:

Simplifying
2x2 + -24x + 146 = 82

Reorder the terms:
146 + -24x + 2x2 = 82

Solving
146 + -24x + 2x2 = 82

Solving for variable 'x'.

Reorder the terms:
146 + -82 + -24x + 2x2 = 82 + -82

Combine like terms: 146 + -82 = 64
64 + -24x + 2x2 = 82 + -82

Combine like terms: 82 + -82 = 0
64 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + -12x + x2) = 0

Factor a trinomial.
2((4 + -1x)(8 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {4, 8}