(x^2-x)(3x+8)=0

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Solution for (x^2-x)(3x+8)=0 equation: 


Simplifying
(x2 + -1x)(3x + 8) = 0

Reorder the terms:
(-1x + x2)(3x + 8) = 0

Reorder the terms:
(-1x + x2)(8 + 3x) = 0

Multiply (-1x + x2) * (8 + 3x)
(-1x * (8 + 3x) + x2(8 + 3x)) = 0
((8 * -1x + 3x * -1x) + x2(8 + 3x)) = 0
((-8x + -3x2) + x2(8 + 3x)) = 0
(-8x + -3x2 + (8 * x2 + 3x * x2)) = 0
(-8x + -3x2 + (8x2 + 3x3)) = 0

Combine like terms: -3x2 + 8x2 = 5x2
(-8x + 5x2 + 3x3) = 0

Solving
-8x + 5x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + 5x + 3x2) = 0

Factor a trinomial.
x((-8 + -3x)(1 + -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 '(-8 + -3x)' equal to zero and attempt to solve:

Simplifying
-8 + -3x = 0

Solving
-8 + -3x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3x = 0 + 8
-3x = 0 + 8

Combine like terms: 0 + 8 = 8
-3x = 8

Divide each side by '-3'.
x = -2.666666667

Simplifying
x = -2.666666667

Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {0, -2.666666667, 1}

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