-2x^2+14x-6=14

Solution for -2x^2+14x-6=14 equation:

Simplifying
-2x2 + 14x + -6 = 14

Reorder the terms:
-6 + 14x + -2x2 = 14

Solving
-6 + 14x + -2x2 = 14

Solving for variable 'x'.

Reorder the terms:
-6 + -14 + 14x + -2x2 = 14 + -14

Combine like terms: -6 + -14 = -20
-20 + 14x + -2x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-20 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 7x + -1x2) = 0

Factor a trinomial.
2((-5 + x)(2 + -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 '(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
Solution
x = {5, 2}