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

Combine like terms: 5x2 + -3x2 = 2x2
4x + 2x2 = -8x + 3x2 + 8x + -3x2

Reorder the terms:
4x + 2x2 = -8x + 8x + 3x2 + -3x2

Combine like terms: -8x + 8x = 0
4x + 2x2 = 0 + 3x2 + -3x2
4x + 2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {0, -2}

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