x(5x-4)=x(3x+8)

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Solution for x(5x-4)=x(3x+8) equation: 


Simplifying
x(5x + -4) = x(3x + 8)

Reorder the terms:
x(-4 + 5x) = x(3x + 8)
(-4 * x + 5x * x) = x(3x + 8)
(-4x + 5x2) = x(3x + 8)

Reorder the terms:
-4x + 5x2 = x(8 + 3x)
-4x + 5x2 = (8 * x + 3x * x)
-4x + 5x2 = (8x + 3x2)

Solving
-4x + 5x2 = 8x + 3x2

Solving for variable 'x'.

Reorder the terms:
-4x + -8x + 5x2 + -3x2 = 8x + 3x2 + -8x + -3x2

Combine like terms: -4x + -8x = -12x
-12x + 5x2 + -3x2 = 8x + 3x2 + -8x + -3x2

Combine like terms: 5x2 + -3x2 = 2x2
-12x + 2x2 = 8x + 3x2 + -8x + -3x2

Reorder the terms:
-12x + 2x2 = 8x + -8x + 3x2 + -3x2

Combine like terms: 8x + -8x = 0
-12x + 2x2 = 0 + 3x2 + -3x2
-12x + 2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-12x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-6 + x) = 0

Ignore the factor 2.

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 '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
Solution
x = {0, 6}

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