2x(x-4)(5x+4)=0

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Solution for 2x(x-4)(5x+4)=0 equation: 


Simplifying
2x(x + -4)(5x + 4) = 0

Reorder the terms:
2x(-4 + x)(5x + 4) = 0

Reorder the terms:
2x(-4 + x)(4 + 5x) = 0

Multiply (-4 + x) * (4 + 5x)
2x(-4(4 + 5x) + x(4 + 5x)) = 0
2x((4 * -4 + 5x * -4) + x(4 + 5x)) = 0
2x((-16 + -20x) + x(4 + 5x)) = 0
2x(-16 + -20x + (4 * x + 5x * x)) = 0
2x(-16 + -20x + (4x + 5x2)) = 0

Combine like terms: -20x + 4x = -16x
2x(-16 + -16x + 5x2) = 0
(-16 * 2x + -16x * 2x + 5x2 * 2x) = 0
(-32x + -32x2 + 10x3) = 0

Solving
-32x + -32x2 + 10x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(-16 + -16x + 5x2) = 0

Factor a trinomial.
2x((-4 + -5x)(4 + -1x)) = 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 '(-4 + -5x)' equal to zero and attempt to solve:

Simplifying
-4 + -5x = 0

Solving
-4 + -5x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5x = 0 + 4
-5x = 0 + 4

Combine like terms: 0 + 4 = 4
-5x = 4

Divide each side by '-5'.
x = -0.8

Simplifying
x = -0.8

Subproblem 3
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {0, -0.8, 4}

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