3p^2-12p-8=7

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Solution for 3p^2-12p-8=7 equation:


Simplifying
3p2 + -12p + -8 = 7

Reorder the terms:
-8 + -12p + 3p2 = 7

Solving
-8 + -12p + 3p2 = 7

Solving for variable 'p'.

Reorder the terms:
-8 + -7 + -12p + 3p2 = 7 + -7

Combine like terms: -8 + -7 = -15
-15 + -12p + 3p2 = 7 + -7

Combine like terms: 7 + -7 = 0
-15 + -12p + 3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -4p + p2) = 0

Factor a trinomial.
3((-1 + -1p)(5 + -1p)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + -1p)' equal to zero and attempt to solve: Simplifying -1 + -1p = 0 Solving -1 + -1p = 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 + -1p = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1p = 0 + 1 -1p = 0 + 1 Combine like terms: 0 + 1 = 1 -1p = 1 Divide each side by '-1'. p = -1 Simplifying p = -1

Subproblem 2

Set the factor '(5 + -1p)' equal to zero and attempt to solve: Simplifying 5 + -1p = 0 Solving 5 + -1p = 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 + -1p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1p = 0 + -5 -1p = 0 + -5 Combine like terms: 0 + -5 = -5 -1p = -5 Divide each side by '-1'. p = 5 Simplifying p = 5

Solution

p = {-1, 5}

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