(x-1)(x+6)=10x

Solution for (x-1)(x+6)=10x equation:

Simplifying
(x + -1)(x + 6) = 10x

Reorder the terms:
(-1 + x)(x + 6) = 10x

Reorder the terms:
(-1 + x)(6 + x) = 10x

Multiply (-1 + x) * (6 + x)
(-1(6 + x) + x(6 + x)) = 10x
((6 * -1 + x * -1) + x(6 + x)) = 10x
((-6 + -1x) + x(6 + x)) = 10x
(-6 + -1x + (6 * x + x * x)) = 10x
(-6 + -1x + (6x + x2)) = 10x

Combine like terms: -1x + 6x = 5x
(-6 + 5x + x2) = 10x

Solving
-6 + 5x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
-6 + 5x + -10x + x2 = 10x + -10x

Combine like terms: 5x + -10x = -5x
-6 + -5x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-6 + -5x + x2 = 0

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