9y^2+5y+39=8y^2+23y-41

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Solution for 9y^2+5y+39=8y^2+23y-41 equation: 


Simplifying
9y2 + 5y + 39 = 8y2 + 23y + -41

Reorder the terms:
39 + 5y + 9y2 = 8y2 + 23y + -41

Reorder the terms:
39 + 5y + 9y2 = -41 + 23y + 8y2

Solving
39 + 5y + 9y2 = -41 + 23y + 8y2

Solving for variable 'y'.

Reorder the terms:
39 + 41 + 5y + -23y + 9y2 + -8y2 = -41 + 23y + 8y2 + 41 + -23y + -8y2

Combine like terms: 39 + 41 = 80
80 + 5y + -23y + 9y2 + -8y2 = -41 + 23y + 8y2 + 41 + -23y + -8y2

Combine like terms: 5y + -23y = -18y
80 + -18y + 9y2 + -8y2 = -41 + 23y + 8y2 + 41 + -23y + -8y2

Combine like terms: 9y2 + -8y2 = 1y2
80 + -18y + 1y2 = -41 + 23y + 8y2 + 41 + -23y + -8y2

Reorder the terms:
80 + -18y + 1y2 = -41 + 41 + 23y + -23y + 8y2 + -8y2

Combine like terms: -41 + 41 = 0
80 + -18y + 1y2 = 0 + 23y + -23y + 8y2 + -8y2
80 + -18y + 1y2 = 23y + -23y + 8y2 + -8y2

Combine like terms: 23y + -23y = 0
80 + -18y + 1y2 = 0 + 8y2 + -8y2
80 + -18y + 1y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
80 + -18y + 1y2 = 0

Factor a trinomial.
(8 + -1y)(10 + -1y) = 0


Subproblem 1
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8

Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {8, 10}

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