x^2-x-5=-6x+1

Solution for x^2-x-5=-6x+1 equation:

Simplifying
x2 + -1x + -5 = -6x + 1

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

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

Solving
-5 + -1x + x2 = 1 + -6x

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(-6 + -1x)(1 + -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 '(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 = {-6, 1}