x(4x-4)=(4x+5x)(x-6)

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Solution for x(4x-4)=(4x+5x)(x-6) equation: 


Simplifying
x(4x + -4) = (4x + 5x)(x + -6)

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

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

Remove parenthesis around (9x)
-4x + 4x2 = 9x(x + -6)

Reorder the terms:
-4x + 4x2 = 9x(-6 + x)
-4x + 4x2 = (-6 * 9x + x * 9x)
-4x + 4x2 = (-54x + 9x2)

Solving
-4x + 4x2 = -54x + 9x2

Solving for variable 'x'.

Reorder the terms:
-4x + 54x + 4x2 + -9x2 = -54x + 9x2 + 54x + -9x2

Combine like terms: -4x + 54x = 50x
50x + 4x2 + -9x2 = -54x + 9x2 + 54x + -9x2

Combine like terms: 4x2 + -9x2 = -5x2
50x + -5x2 = -54x + 9x2 + 54x + -9x2

Reorder the terms:
50x + -5x2 = -54x + 54x + 9x2 + -9x2

Combine like terms: -54x + 54x = 0
50x + -5x2 = 0 + 9x2 + -9x2
50x + -5x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
50x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5x'.
5x(10 + -1x) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0, 10}

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