x^2-13x+1=-8x-5

Solution for x^2-13x+1=-8x-5 equation:

Simplifying
x2 + -13x + 1 = -8x + -5

Reorder the terms:
1 + -13x + x2 = -8x + -5

Reorder the terms:
1 + -13x + x2 = -5 + -8x

Solving
1 + -13x + x2 = -5 + -8x

Solving for variable 'x'.

Reorder the terms:
1 + 5 + -13x + 8x + x2 = -5 + -8x + 5 + 8x

Combine like terms: 1 + 5 = 6
6 + -13x + 8x + x2 = -5 + -8x + 5 + 8x

Combine like terms: -13x + 8x = -5x
6 + -5x + x2 = -5 + -8x + 5 + 8x

Reorder the terms:
6 + -5x + x2 = -5 + 5 + -8x + 8x

Combine like terms: -5 + 5 = 0
6 + -5x + x2 = 0 + -8x + 8x
6 + -5x + x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
6 + -5x + x2 = 0

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

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 '(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 = {2, 3}