(8p+2)(4p-5)=

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Solution for (8p+2)(4p-5)= equation:


Simplifying
(8p + 2)(4p + -5) = 0

Reorder the terms:
(2 + 8p)(4p + -5) = 0

Reorder the terms:
(2 + 8p)(-5 + 4p) = 0

Multiply (2 + 8p) * (-5 + 4p)
(2(-5 + 4p) + 8p * (-5 + 4p)) = 0
((-5 * 2 + 4p * 2) + 8p * (-5 + 4p)) = 0
((-10 + 8p) + 8p * (-5 + 4p)) = 0
(-10 + 8p + (-5 * 8p + 4p * 8p)) = 0
(-10 + 8p + (-40p + 32p2)) = 0

Combine like terms: 8p + -40p = -32p
(-10 + -32p + 32p2) = 0

Solving
-10 + -32p + 32p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -16p + 16p2) = 0

Factor a trinomial.
2((-1 + -4p)(5 + -4p)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -4p)' equal to zero and attempt to solve: Simplifying -1 + -4p = 0 Solving -1 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4p = 0 + 1 -4p = 0 + 1 Combine like terms: 0 + 1 = 1 -4p = 1 Divide each side by '-4'. p = -0.25 Simplifying p = -0.25

Subproblem 2

Set the factor '(5 + -4p)' equal to zero and attempt to solve: Simplifying 5 + -4p = 0 Solving 5 + -4p = 0 Move all terms containing p to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4p = 0 + -5 -4p = 0 + -5 Combine like terms: 0 + -5 = -5 -4p = -5 Divide each side by '-4'. p = 1.25 Simplifying p = 1.25

Solution

p = {-0.25, 1.25}

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