(y+5)(y+5)=2y^2+3y+37

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Solution for (y+5)(y+5)=2y^2+3y+37 equation: 


Simplifying
(y + 5)(y + 5) = 2y2 + 3y + 37

Reorder the terms:
(5 + y)(y + 5) = 2y2 + 3y + 37

Reorder the terms:
(5 + y)(5 + y) = 2y2 + 3y + 37

Multiply (5 + y) * (5 + y)
(5(5 + y) + y(5 + y)) = 2y2 + 3y + 37
((5 * 5 + y * 5) + y(5 + y)) = 2y2 + 3y + 37
((25 + 5y) + y(5 + y)) = 2y2 + 3y + 37
(25 + 5y + (5 * y + y * y)) = 2y2 + 3y + 37
(25 + 5y + (5y + y2)) = 2y2 + 3y + 37

Combine like terms: 5y + 5y = 10y
(25 + 10y + y2) = 2y2 + 3y + 37

Reorder the terms:
25 + 10y + y2 = 37 + 3y + 2y2

Solving
25 + 10y + y2 = 37 + 3y + 2y2

Solving for variable 'y'.

Reorder the terms:
25 + -37 + 10y + -3y + y2 + -2y2 = 37 + 3y + 2y2 + -37 + -3y + -2y2

Combine like terms: 25 + -37 = -12
-12 + 10y + -3y + y2 + -2y2 = 37 + 3y + 2y2 + -37 + -3y + -2y2

Combine like terms: 10y + -3y = 7y
-12 + 7y + y2 + -2y2 = 37 + 3y + 2y2 + -37 + -3y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-12 + 7y + -1y2 = 37 + 3y + 2y2 + -37 + -3y + -2y2

Reorder the terms:
-12 + 7y + -1y2 = 37 + -37 + 3y + -3y + 2y2 + -2y2

Combine like terms: 37 + -37 = 0
-12 + 7y + -1y2 = 0 + 3y + -3y + 2y2 + -2y2
-12 + 7y + -1y2 = 3y + -3y + 2y2 + -2y2

Combine like terms: 3y + -3y = 0
-12 + 7y + -1y2 = 0 + 2y2 + -2y2
-12 + 7y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-12 + 7y + -1y2 = 0

Factor a trinomial.
(-4 + y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-4 + y)' equal to zero and attempt to solve:

Simplifying
-4 + y = 0

Solving
-4 + y = 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 + y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + y = 0 + 4
y = 0 + 4

Combine like terms: 0 + 4 = 4
y = 4

Simplifying
y = 4

Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {4, 3}

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