(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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