4y^2+20y+25=15-2y

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Solution for 4y^2+20y+25=15-2y equation: 


Simplifying
4y2 + 20y + 25 = 15 + -2y

Reorder the terms:
25 + 20y + 4y2 = 15 + -2y

Solving
25 + 20y + 4y2 = 15 + -2y

Solving for variable 'y'.

Reorder the terms:
25 + -15 + 20y + 2y + 4y2 = 15 + -2y + -15 + 2y

Combine like terms: 25 + -15 = 10
10 + 20y + 2y + 4y2 = 15 + -2y + -15 + 2y

Combine like terms: 20y + 2y = 22y
10 + 22y + 4y2 = 15 + -2y + -15 + 2y

Reorder the terms:
10 + 22y + 4y2 = 15 + -15 + -2y + 2y

Combine like terms: 15 + -15 = 0
10 + 22y + 4y2 = 0 + -2y + 2y
10 + 22y + 4y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
10 + 22y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 11y + 2y2) = 0

Factor a trinomial.
2((5 + y)(1 + 2y)) = 0

Ignore the factor 2.

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 '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 2y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2y = 0 + -1
2y = 0 + -1

Combine like terms: 0 + -1 = -1
2y = -1

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-5, -0.5}

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