15p^2=28p-5

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Solution for 15p^2=28p-5 equation:


Simplifying
15p2 = 28p + -5

Reorder the terms:
15p2 = -5 + 28p

Solving
15p2 = -5 + 28p

Solving for variable 'p'.

Reorder the terms:
5 + -28p + 15p2 = -5 + 28p + 5 + -28p

Reorder the terms:
5 + -28p + 15p2 = -5 + 5 + 28p + -28p

Combine like terms: -5 + 5 = 0
5 + -28p + 15p2 = 0 + 28p + -28p
5 + -28p + 15p2 = 28p + -28p

Combine like terms: 28p + -28p = 0
5 + -28p + 15p2 = 0

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

Subproblem 1

Set the factor '(1 + -5p)' equal to zero and attempt to solve: Simplifying 1 + -5p = 0 Solving 1 + -5p = 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 + -5p = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5p = 0 + -1 -5p = 0 + -1 Combine like terms: 0 + -1 = -1 -5p = -1 Divide each side by '-5'. p = 0.2 Simplifying p = 0.2

Subproblem 2

Set the factor '(5 + -3p)' equal to zero and attempt to solve: Simplifying 5 + -3p = 0 Solving 5 + -3p = 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 + -3p = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3p = 0 + -5 -3p = 0 + -5 Combine like terms: 0 + -5 = -5 -3p = -5 Divide each side by '-3'. p = 1.666666667 Simplifying p = 1.666666667

Solution

p = {0.2, 1.666666667}

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