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

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


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

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

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

Multiply (p + 2x) * (-5p + 4x)
px(p(-5p + 4x) + 2x * (-5p + 4x)) = 0
px((-5p * p + 4x * p) + 2x * (-5p + 4x)) = 0

Reorder the terms:
px((4px + -5p2) + 2x * (-5p + 4x)) = 0
px((4px + -5p2) + 2x * (-5p + 4x)) = 0
px(4px + -5p2 + (-5p * 2x + 4x * 2x)) = 0
px(4px + -5p2 + (-10px + 8x2)) = 0

Reorder the terms:
px(4px + -10px + -5p2 + 8x2) = 0

Combine like terms: 4px + -10px = -6px
px(-6px + -5p2 + 8x2) = 0
(-6px * px + -5p2 * px + 8x2 * px) = 0

Reorder the terms:
(8px3 + -6p2x2 + -5p3x) = 0
(8px3 + -6p2x2 + -5p3x) = 0

Solving
8px3 + -6p2x2 + -5p3x = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'px'.
px(8x2 + -6px + -5p2) = 0

Factor a trinomial.
px((4x + -5p)(2x + p)) = 0


Subproblem 1
Set the factor 'px' equal to zero and attempt to solve:

Simplifying
px = 0

Solving
px = 0

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

Simplifying
px = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4x + -5p)' equal to zero and attempt to solve:

Simplifying
4x + -5p = 0

Reorder the terms:
-5p + 4x = 0

Solving
-5p + 4x = 0

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

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

Combine like terms: 4x + -4x = 0
-5p + 0 = 0 + -4x
-5p = 0 + -4x
Remove the zero:
-5p = -4x

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

Simplifying
p = 0.8x

Subproblem 3
Set the factor '(2x + p)' equal to zero and attempt to solve:

Simplifying
2x + p = 0

Reorder the terms:
p + 2x = 0

Solving
p + 2x = 0

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

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

Combine like terms: 2x + -2x = 0
p + 0 = 0 + -2x
p = 0 + -2x
Remove the zero:
p = -2x

Simplifying
p = -2x
Solution
p = {0.8x, -2x}

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