(5x)(11x)=(8x)(7x-4)

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Solution for (5x)(11x)=(8x)(7x-4) equation: 


Simplifying
(5x)(11x) = (8x)(7x + -4)

Remove parenthesis around (5x)
5x(11x) = (8x)(7x + -4)

Remove parenthesis around (11x)
5x * 11x = (8x)(7x + -4)

Reorder the terms for easier multiplication:
5 * 11x * x = (8x)(7x + -4)

Multiply 5 * 11
55x * x = (8x)(7x + -4)

Multiply x * x
55x2 = (8x)(7x + -4)

Remove parenthesis around (8x)
55x2 = 8x(7x + -4)

Reorder the terms:
55x2 = 8x(-4 + 7x)
55x2 = (-4 * 8x + 7x * 8x)
55x2 = (-32x + 56x2)

Solving
55x2 = -32x + 56x2

Solving for variable 'x'.

Reorder the terms:
32x + 55x2 + -56x2 = -32x + 56x2 + 32x + -56x2

Combine like terms: 55x2 + -56x2 = -1x2
32x + -1x2 = -32x + 56x2 + 32x + -56x2

Reorder the terms:
32x + -1x2 = -32x + 32x + 56x2 + -56x2

Combine like terms: -32x + 32x = 0
32x + -1x2 = 0 + 56x2 + -56x2
32x + -1x2 = 56x2 + -56x2

Combine like terms: 56x2 + -56x2 = 0
32x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(32 + -1x) = 0


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 '(32 + -1x)' equal to zero and attempt to solve:

Simplifying
32 + -1x = 0

Solving
32 + -1x = 0

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

Add '-32' to each side of the equation.
32 + -32 + -1x = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -1x = 0 + -32
-1x = 0 + -32

Combine like terms: 0 + -32 = -32
-1x = -32

Divide each side by '-1'.
x = 32

Simplifying
x = 32
Solution
x = {0, 32}

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