(7x)(6x)=5x(10x-4)

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Solution for (7x)(6x)=5x(10x-4) equation: 


Simplifying
(7x)(6x) = 5x(10x + -4)

Remove parenthesis around (7x)
7x(6x) = 5x(10x + -4)

Remove parenthesis around (6x)
7x * 6x = 5x(10x + -4)

Reorder the terms for easier multiplication:
7 * 6x * x = 5x(10x + -4)

Multiply 7 * 6
42x * x = 5x(10x + -4)

Multiply x * x
42x2 = 5x(10x + -4)

Reorder the terms:
42x2 = 5x(-4 + 10x)
42x2 = (-4 * 5x + 10x * 5x)
42x2 = (-20x + 50x2)

Solving
42x2 = -20x + 50x2

Solving for variable 'x'.

Reorder the terms:
20x + 42x2 + -50x2 = -20x + 50x2 + 20x + -50x2

Combine like terms: 42x2 + -50x2 = -8x2
20x + -8x2 = -20x + 50x2 + 20x + -50x2

Reorder the terms:
20x + -8x2 = -20x + 20x + 50x2 + -50x2

Combine like terms: -20x + 20x = 0
20x + -8x2 = 0 + 50x2 + -50x2
20x + -8x2 = 50x2 + -50x2

Combine like terms: 50x2 + -50x2 = 0
20x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(5 + -2x) = 0

Ignore the factor 4.

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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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