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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -13 + 4 = -9
-9 + 13x + -5x + x2 = -4 + 5x + 4 + -5x

Combine like terms: 13x + -5x = 8x
-9 + 8x + x2 = -4 + 5x + 4 + -5x

Reorder the terms:
-9 + 8x + x2 = -4 + 4 + 5x + -5x

Combine like terms: -4 + 4 = 0
-9 + 8x + x2 = 0 + 5x + -5x
-9 + 8x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-9 + 8x + x2 = 0

Factor a trinomial.
(-9 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 1}