-6p^2-14p=-24-8p^2

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Solution for -6p^2-14p=-24-8p^2 equation:


Simplifying
-6p2 + -14p = -24 + -8p2

Reorder the terms:
-14p + -6p2 = -24 + -8p2

Solving
-14p + -6p2 = -24 + -8p2

Solving for variable 'p'.

Reorder the terms:
24 + -14p + -6p2 + 8p2 = -24 + -8p2 + 24 + 8p2

Combine like terms: -6p2 + 8p2 = 2p2
24 + -14p + 2p2 = -24 + -8p2 + 24 + 8p2

Reorder the terms:
24 + -14p + 2p2 = -24 + 24 + -8p2 + 8p2

Combine like terms: -24 + 24 = 0
24 + -14p + 2p2 = 0 + -8p2 + 8p2
24 + -14p + 2p2 = -8p2 + 8p2

Combine like terms: -8p2 + 8p2 = 0
24 + -14p + 2p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -7p + p2) = 0

Factor a trinomial.
2((3 + -1p)(4 + -1p)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3 + -1p)' equal to zero and attempt to solve: Simplifying 3 + -1p = 0 Solving 3 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1p = 0 + -3 -1p = 0 + -3 Combine like terms: 0 + -3 = -3 -1p = -3 Divide each side by '-1'. p = 3 Simplifying p = 3

Subproblem 2

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

Solution

p = {3, 4}

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