-y^2=10y+25

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Solution for -y^2=10y+25 equation:


Simplifying
-1y2 = 10y + 25

Reorder the terms:
-1y2 = 25 + 10y

Solving
-1y2 = 25 + 10y

Solving for variable 'y'.

Reorder the terms:
-25 + -10y + -1y2 = 25 + 10y + -25 + -10y

Reorder the terms:
-25 + -10y + -1y2 = 25 + -25 + 10y + -10y

Combine like terms: 25 + -25 = 0
-25 + -10y + -1y2 = 0 + 10y + -10y
-25 + -10y + -1y2 = 10y + -10y

Combine like terms: 10y + -10y = 0
-25 + -10y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 10y + y2) = 0

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

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5

Subproblem 2

Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5

Solution

y = {-5, -5}

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