(x-1)(x+6)=4x

Solution for (x-1)(x+6)=4x equation:

Simplifying
(x + -1)(x + 6) = 4x

Reorder the terms:
(-1 + x)(x + 6) = 4x

Reorder the terms:
(-1 + x)(6 + x) = 4x

Multiply (-1 + x) * (6 + x)
(-1(6 + x) + x(6 + x)) = 4x
((6 * -1 + x * -1) + x(6 + x)) = 4x
((-6 + -1x) + x(6 + x)) = 4x
(-6 + -1x + (6 * x + x * x)) = 4x
(-6 + -1x + (6x + x2)) = 4x

Combine like terms: -1x + 6x = 5x
(-6 + 5x + x2) = 4x

Solving
-6 + 5x + x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-6 + 5x + -4x + x2 = 4x + -4x

Combine like terms: 5x + -4x = 1x
-6 + 1x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-6 + 1x + x2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-3, 2}