7p^2=-38p-15

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Solution for 7p^2=-38p-15 equation:


Simplifying
7p2 = -38p + -15

Reorder the terms:
7p2 = -15 + -38p

Solving
7p2 = -15 + -38p

Solving for variable 'p'.

Reorder the terms:
15 + 38p + 7p2 = -15 + -38p + 15 + 38p

Reorder the terms:
15 + 38p + 7p2 = -15 + 15 + -38p + 38p

Combine like terms: -15 + 15 = 0
15 + 38p + 7p2 = 0 + -38p + 38p
15 + 38p + 7p2 = -38p + 38p

Combine like terms: -38p + 38p = 0
15 + 38p + 7p2 = 0

Factor a trinomial.
(5 + p)(3 + 7p) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(3 + 7p)' equal to zero and attempt to solve: Simplifying 3 + 7p = 0 Solving 3 + 7p = 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 + 7p = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7p = 0 + -3 7p = 0 + -3 Combine like terms: 0 + -3 = -3 7p = -3 Divide each side by '7'. p = -0.4285714286 Simplifying p = -0.4285714286

Solution

p = {-5, -0.4285714286}

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