9x(4x+8)=4x(10x-2)

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Solution for 9x(4x+8)=4x(10x-2) equation: 


Simplifying
9x(4x + 8) = 4x(10x + -2)

Reorder the terms:
9x(8 + 4x) = 4x(10x + -2)
(8 * 9x + 4x * 9x) = 4x(10x + -2)
(72x + 36x2) = 4x(10x + -2)

Reorder the terms:
72x + 36x2 = 4x(-2 + 10x)
72x + 36x2 = (-2 * 4x + 10x * 4x)
72x + 36x2 = (-8x + 40x2)

Solving
72x + 36x2 = -8x + 40x2

Solving for variable 'x'.

Reorder the terms:
72x + 8x + 36x2 + -40x2 = -8x + 40x2 + 8x + -40x2

Combine like terms: 72x + 8x = 80x
80x + 36x2 + -40x2 = -8x + 40x2 + 8x + -40x2

Combine like terms: 36x2 + -40x2 = -4x2
80x + -4x2 = -8x + 40x2 + 8x + -40x2

Reorder the terms:
80x + -4x2 = -8x + 8x + 40x2 + -40x2

Combine like terms: -8x + 8x = 0
80x + -4x2 = 0 + 40x2 + -40x2
80x + -4x2 = 40x2 + -40x2

Combine like terms: 40x2 + -40x2 = 0
80x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(20 + -1x) = 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 '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Solution
x = {0, 20}

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