p^2-20p+27=-9

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Solution for p^2-20p+27=-9 equation:


Simplifying
p2 + -20p + 27 = -9

Reorder the terms:
27 + -20p + p2 = -9

Solving
27 + -20p + p2 = -9

Solving for variable 'p'.

Reorder the terms:
27 + 9 + -20p + p2 = -9 + 9

Combine like terms: 27 + 9 = 36
36 + -20p + p2 = -9 + 9

Combine like terms: -9 + 9 = 0
36 + -20p + p2 = 0

Factor a trinomial.
(2 + -1p)(18 + -1p) = 0

Subproblem 1

Set the factor '(2 + -1p)' equal to zero and attempt to solve: Simplifying 2 + -1p = 0 Solving 2 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1p = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1p = 0 + -2 -1p = 0 + -2 Combine like terms: 0 + -2 = -2 -1p = -2 Divide each side by '-1'. p = 2 Simplifying p = 2

Subproblem 2

Set the factor '(18 + -1p)' equal to zero and attempt to solve: Simplifying 18 + -1p = 0 Solving 18 + -1p = 0 Move all terms containing p to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1p = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1p = 0 + -18 -1p = 0 + -18 Combine like terms: 0 + -18 = -18 -1p = -18 Divide each side by '-1'. p = 18 Simplifying p = 18

Solution

p = {2, 18}

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