5x(x-1)=(2x+6)(x-1)

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

Simplifying
5x(x + -1) = (2x + 6)(x + -1)

Reorder the terms:
5x(-1 + x) = (2x + 6)(x + -1)
(-1 * 5x + x * 5x) = (2x + 6)(x + -1)
(-5x + 5x2) = (2x + 6)(x + -1)

Reorder the terms:
-5x + 5x2 = (6 + 2x)(x + -1)

Reorder the terms:
-5x + 5x2 = (6 + 2x)(-1 + x)

Multiply (6 + 2x) * (-1 + x)
-5x + 5x2 = (6(-1 + x) + 2x * (-1 + x))
-5x + 5x2 = ((-1 * 6 + x * 6) + 2x * (-1 + x))
-5x + 5x2 = ((-6 + 6x) + 2x * (-1 + x))
-5x + 5x2 = (-6 + 6x + (-1 * 2x + x * 2x))
-5x + 5x2 = (-6 + 6x + (-2x + 2x2))

Combine like terms: 6x + -2x = 4x
-5x + 5x2 = (-6 + 4x + 2x2)

Solving
-5x + 5x2 = -6 + 4x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -5x + -4x + 5x2 + -2x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2

Combine like terms: -5x + -4x = -9x
6 + -9x + 5x2 + -2x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2

Combine like terms: 5x2 + -2x2 = 3x2
6 + -9x + 3x2 = -6 + 4x + 2x2 + 6 + -4x + -2x2

Reorder the terms:
6 + -9x + 3x2 = -6 + 6 + 4x + -4x + 2x2 + -2x2

Combine like terms: -6 + 6 = 0
6 + -9x + 3x2 = 0 + 4x + -4x + 2x2 + -2x2
6 + -9x + 3x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
6 + -9x + 3x2 = 0 + 2x2 + -2x2
6 + -9x + 3x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
6 + -9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -3x + x2) = 0

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

Ignore the factor 3.
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 '(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 = {1, 2}