2x^2-1=14-x

Solution for 2x^2-1=14-x equation:

Simplifying
2x2 + -1 = 14 + -1x

Reorder the terms:
-1 + 2x2 = 14 + -1x

Solving
-1 + 2x2 = 14 + -1x

Solving for variable 'x'.

Reorder the terms:
-1 + -14 + x + 2x2 = 14 + -1x + -14 + x

Combine like terms: -1 + -14 = -15
-15 + x + 2x2 = 14 + -1x + -14 + x

Reorder the terms:
-15 + x + 2x2 = 14 + -14 + -1x + x

Combine like terms: 14 + -14 = 0
-15 + x + 2x2 = 0 + -1x + x
-15 + x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-15 + x + 2x2 = 0

Factor a trinomial.
(-3 + -1x)(5 + -2x) = 0

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-3, 2.5}