(8p^2-5p)[-2(3p^2-2p+4)]=0

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Solution for (8p^2-5p)[-2(3p^2-2p+4)]=0 equation: 


Simplifying
(8p2 + -5p)[-2(3p2 + -2p + 4)] = 0

Reorder the terms:
(-5p + 8p2)[-2(3p2 + -2p + 4)] = 0

Reorder the terms:
(-5p + 8p2)[-2(4 + -2p + 3p2)] = 0
(-5p + 8p2)[(4 * -2 + -2p * -2 + 3p2 * -2)] = 0
(-5p + 8p2)[(-8 + 4p + -6p2)] = 0

Multiply (-5p + 8p2) * [-8 + 4p + -6p2]
(-5p * [-8 + 4p + -6p2] + 8p2 * [-8 + 4p + -6p2]) = 0
([-8 * -5p + 4p * -5p + -6p2 * -5p] + 8p2 * [-8 + 4p + -6p2]) = 0
([40p + -20p2 + 30p3] + 8p2 * [-8 + 4p + -6p2]) = 0
(40p + -20p2 + 30p3 + [-8 * 8p2 + 4p * 8p2 + -6p2 * 8p2]) = 0
(40p + -20p2 + 30p3 + [-64p2 + 32p3 + -48p4]) = 0

Reorder the terms:
(40p + -20p2 + -64p2 + 30p3 + 32p3 + -48p4) = 0

Combine like terms: -20p2 + -64p2 = -84p2
(40p + -84p2 + 30p3 + 32p3 + -48p4) = 0

Combine like terms: 30p3 + 32p3 = 62p3
(40p + -84p2 + 62p3 + -48p4) = 0

Solving
40p + -84p2 + 62p3 + -48p4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2p'.
2p(20 + -42p + 31p2 + -24p3) = 0

Ignore the factor 2.

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

Simplifying
p = 0

Solving
p = 0

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

Simplifying
p = 0

Subproblem 2
Set the factor '(20 + -42p + 31p2 + -24p3)' equal to zero and attempt to solve:

Simplifying
20 + -42p + 31p2 + -24p3 = 0

Solving
20 + -42p + 31p2 + -24p3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {0}

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