(2y+15)*(2y+15)+y^2=50

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Solution for (2y+15)*(2y+15)+y^2=50 equation: 


Simplifying
(2y + 15)(2y + 15) + y2 = 50

Reorder the terms:
(15 + 2y)(2y + 15) + y2 = 50

Reorder the terms:
(15 + 2y)(15 + 2y) + y2 = 50

Multiply (15 + 2y) * (15 + 2y)
(15(15 + 2y) + 2y * (15 + 2y)) + y2 = 50
((15 * 15 + 2y * 15) + 2y * (15 + 2y)) + y2 = 50
((225 + 30y) + 2y * (15 + 2y)) + y2 = 50
(225 + 30y + (15 * 2y + 2y * 2y)) + y2 = 50
(225 + 30y + (30y + 4y2)) + y2 = 50

Combine like terms: 30y + 30y = 60y
(225 + 60y + 4y2) + y2 = 50

Combine like terms: 4y2 + y2 = 5y2
225 + 60y + 5y2 = 50

Solving
225 + 60y + 5y2 = 50

Solving for variable 'y'.

Reorder the terms:
225 + -50 + 60y + 5y2 = 50 + -50

Combine like terms: 225 + -50 = 175
175 + 60y + 5y2 = 50 + -50

Combine like terms: 50 + -50 = 0
175 + 60y + 5y2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(35 + 12y + y2) = 0

Factor a trinomial.
5((7 + y)(5 + y)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7

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 = {-7, -5}

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