x^2+4x-5=x+13

Solution for x^2+4x-5=x+13 equation:

Simplifying
x2 + 4x + -5 = x + 13

Reorder the terms:
-5 + 4x + x2 = x + 13

Reorder the terms:
-5 + 4x + x2 = 13 + x

Solving
-5 + 4x + x2 = 13 + x

Solving for variable 'x'.

Reorder the terms:
-5 + -13 + 4x + -1x + x2 = 13 + x + -13 + -1x

Combine like terms: -5 + -13 = -18
-18 + 4x + -1x + x2 = 13 + x + -13 + -1x

Combine like terms: 4x + -1x = 3x
-18 + 3x + x2 = 13 + x + -13 + -1x

Reorder the terms:
-18 + 3x + x2 = 13 + -13 + x + -1x

Combine like terms: 13 + -13 = 0
-18 + 3x + x2 = 0 + x + -1x
-18 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-18 + 3x + x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0

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

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 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 + -1x = 0 + 6

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

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

Divide each side by '-1'.
x = -6

Simplifying
x = -6
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 = {-6, 3}