(5*y*y)+(5*y)=100

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Solution for (5*y*y)+(5*y)=100 equation:


Simplifying
(5y * y) + (5y) = 100

Multiply y * y
(5y2) + (5y) = 100

Reorder the terms:
(5y) + (5y2) = 100

Solving
(5y) + (5y2) = 100

Solving for variable 'y'.

Reorder the terms:
-100 + (5y) + (5y2) = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + (5y) + (5y2) = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + y + y2) = 0

Factor a trinomial.
5((-5 + -1y)(4 + -1y)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(4 + -1y)' equal to zero and attempt to solve: Simplifying 4 + -1y = 0 Solving 4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y = 0 + -4 -1y = 0 + -4 Combine like terms: 0 + -4 = -4 -1y = -4 Divide each side by '-1'. y = 4 Simplifying y = 4

Solution

y = {-5, 4}

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