x*(4x+1)*(x-8)=0

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Solution for x*(4x+1)*(x-8)=0 equation: 


Simplifying
x(4x + 1)(x + -8) = 0

Reorder the terms:
x(1 + 4x)(x + -8) = 0

Reorder the terms:
x(1 + 4x)(-8 + x) = 0

Multiply (1 + 4x) * (-8 + x)
x(1(-8 + x) + 4x * (-8 + x)) = 0
x((-8 * 1 + x * 1) + 4x * (-8 + x)) = 0
x((-8 + 1x) + 4x * (-8 + x)) = 0
x(-8 + 1x + (-8 * 4x + x * 4x)) = 0
x(-8 + 1x + (-32x + 4x2)) = 0

Combine like terms: 1x + -32x = -31x
x(-8 + -31x + 4x2) = 0
(-8 * x + -31x * x + 4x2 * x) = 0
(-8x + -31x2 + 4x3) = 0

Solving
-8x + -31x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-8 + -31x + 4x2) = 0

Factor a trinomial.
x((-1 + -4x)(8 + -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 '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, -0.25, 8}

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