2x^2-1=4x+15

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Solution for 2x^2-1=4x+15 equation: 


Simplifying
2x2 + -1 = 4x + 15

Reorder the terms:
-1 + 2x2 = 4x + 15

Reorder the terms:
-1 + 2x2 = 15 + 4x

Solving
-1 + 2x2 = 15 + 4x

Solving for variable 'x'.

Reorder the terms:
-1 + -15 + -4x + 2x2 = 15 + 4x + -15 + -4x

Combine like terms: -1 + -15 = -16
-16 + -4x + 2x2 = 15 + 4x + -15 + -4x

Reorder the terms:
-16 + -4x + 2x2 = 15 + -15 + 4x + -4x

Combine like terms: 15 + -15 = 0
-16 + -4x + 2x2 = 0 + 4x + -4x
-16 + -4x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-16 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(4 + -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 '(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
Solution
x = {-2, 4}

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