5x^2-1=x+5

Solution for 5x^2-1=x+5 equation:

Simplifying
5x2 + -1 = x + 5

Reorder the terms:
-1 + 5x2 = x + 5

Reorder the terms:
-1 + 5x2 = 5 + x

Solving
-1 + 5x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -5 + -1x + 5x2 = 5 + x + -5 + -1x

Combine like terms: -1 + -5 = -6
-6 + -1x + 5x2 = 5 + x + -5 + -1x

Reorder the terms:
-6 + -1x + 5x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
-6 + -1x + 5x2 = 0 + x + -1x
-6 + -1x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-6 + -1x + 5x2 = 0

Factor a trinomial.
(-1 + -1x)(6 + -5x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-1, 1.2}