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

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


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

Reorder the terms:
6x(-1 + x) = (4 + x)(x + -1)
(-1 * 6x + x * 6x) = (4 + x)(x + -1)
(-6x + 6x2) = (4 + x)(x + -1)

Reorder the terms:
-6x + 6x2 = (4 + x)(-1 + x)

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

Combine like terms: 4x + -1x = 3x
-6x + 6x2 = (-4 + 3x + x2)

Solving
-6x + 6x2 = -4 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
4 + -6x + -3x + 6x2 + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: -6x + -3x = -9x
4 + -9x + 6x2 + -1x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Combine like terms: 6x2 + -1x2 = 5x2
4 + -9x + 5x2 = -4 + 3x + x2 + 4 + -3x + -1x2

Reorder the terms:
4 + -9x + 5x2 = -4 + 4 + 3x + -3x + x2 + -1x2

Combine like terms: -4 + 4 = 0
4 + -9x + 5x2 = 0 + 3x + -3x + x2 + -1x2
4 + -9x + 5x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
4 + -9x + 5x2 = 0 + x2 + -1x2
4 + -9x + 5x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -9x + 5x2 = 0

Factor a trinomial.
(4 + -5x)(1 + -1x) = 0


Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

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 = {0.8, 1}

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