30-10p+p*p=9

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Solution for 30-10p+p*p=9 equation:


Simplifying
30 + -10p + p * p = 9

Multiply p * p
30 + -10p + p2 = 9

Solving
30 + -10p + p2 = 9

Solving for variable 'p'.

Reorder the terms:
30 + -9 + -10p + p2 = 9 + -9

Combine like terms: 30 + -9 = 21
21 + -10p + p2 = 9 + -9

Combine like terms: 9 + -9 = 0
21 + -10p + p2 = 0

Factor a trinomial.
(3 + -1p)(7 + -1p) = 0

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 '(7 + -1p)' equal to zero and attempt to solve: Simplifying 7 + -1p = 0 Solving 7 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1p = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1p = 0 + -7 -1p = 0 + -7 Combine like terms: 0 + -7 = -7 -1p = -7 Divide each side by '-1'. p = 7 Simplifying p = 7

Solution

p = {3, 7}

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