2(2y-5)+y^2-62=180

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Solution for 2(2y-5)+y^2-62=180 equation: 


Simplifying
2(2y + -5) + y2 + -62 = 180

Reorder the terms:
2(-5 + 2y) + y2 + -62 = 180
(-5 * 2 + 2y * 2) + y2 + -62 = 180
(-10 + 4y) + y2 + -62 = 180

Reorder the terms:
-10 + -62 + 4y + y2 = 180

Combine like terms: -10 + -62 = -72
-72 + 4y + y2 = 180

Solving
-72 + 4y + y2 = 180

Solving for variable 'y'.

Reorder the terms:
-72 + -180 + 4y + y2 = 180 + -180

Combine like terms: -72 + -180 = -252
-252 + 4y + y2 = 180 + -180

Combine like terms: 180 + -180 = 0
-252 + 4y + y2 = 0

Factor a trinomial.
(-18 + -1y)(14 + -1y) = 0


Subproblem 1
Set the factor '(-18 + -1y)' equal to zero and attempt to solve:

Simplifying
-18 + -1y = 0

Solving
-18 + -1y = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1y = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1y = 0 + 18
-1y = 0 + 18

Combine like terms: 0 + 18 = 18
-1y = 18

Divide each side by '-1'.
y = -18

Simplifying
y = -18

Subproblem 2
Set the factor '(14 + -1y)' equal to zero and attempt to solve:

Simplifying
14 + -1y = 0

Solving
14 + -1y = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1y = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1y = 0 + -14
-1y = 0 + -14

Combine like terms: 0 + -14 = -14
-1y = -14

Divide each side by '-1'.
y = 14

Simplifying
y = 14
Solution
y = {-18, 14}

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