5p^2-11p+27=-p+2+4p^2

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Solution for 5p^2-11p+27=-p+2+4p^2 equation:


Simplifying
5p2 + -11p + 27 = -1p + 2 + 4p2

Reorder the terms:
27 + -11p + 5p2 = -1p + 2 + 4p2

Reorder the terms:
27 + -11p + 5p2 = 2 + -1p + 4p2

Solving
27 + -11p + 5p2 = 2 + -1p + 4p2

Solving for variable 'p'.

Reorder the terms:
27 + -2 + -11p + p + 5p2 + -4p2 = 2 + -1p + 4p2 + -2 + p + -4p2

Combine like terms: 27 + -2 = 25
25 + -11p + p + 5p2 + -4p2 = 2 + -1p + 4p2 + -2 + p + -4p2

Combine like terms: -11p + p = -10p
25 + -10p + 5p2 + -4p2 = 2 + -1p + 4p2 + -2 + p + -4p2

Combine like terms: 5p2 + -4p2 = 1p2
25 + -10p + 1p2 = 2 + -1p + 4p2 + -2 + p + -4p2

Reorder the terms:
25 + -10p + 1p2 = 2 + -2 + -1p + p + 4p2 + -4p2

Combine like terms: 2 + -2 = 0
25 + -10p + 1p2 = 0 + -1p + p + 4p2 + -4p2
25 + -10p + 1p2 = -1p + p + 4p2 + -4p2

Combine like terms: -1p + p = 0
25 + -10p + 1p2 = 0 + 4p2 + -4p2
25 + -10p + 1p2 = 4p2 + -4p2

Combine like terms: 4p2 + -4p2 = 0
25 + -10p + 1p2 = 0

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

Subproblem 1

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

Subproblem 2

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

Solution

p = {5, 5}

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