2x^2-2x+14=26

Solution for 2x^2-2x+14=26 equation:

Simplifying
2x2 + -2x + 14 = 26

Reorder the terms:
14 + -2x + 2x2 = 26

Solving
14 + -2x + 2x2 = 26

Solving for variable 'x'.

Reorder the terms:
14 + -26 + -2x + 2x2 = 26 + -26

Combine like terms: 14 + -26 = -12
-12 + -2x + 2x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-12 + -2x + 2x2 = 0

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

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

Ignore the factor 2.
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 '(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 = {-2, 3}