2y^2+5y=3y^2-2y-18

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Solution for 2y^2+5y=3y^2-2y-18 equation: 


Simplifying
2y2 + 5y = 3y2 + -2y + -18

Reorder the terms:
5y + 2y2 = 3y2 + -2y + -18

Reorder the terms:
5y + 2y2 = -18 + -2y + 3y2

Solving
5y + 2y2 = -18 + -2y + 3y2

Solving for variable 'y'.

Reorder the terms:
18 + 5y + 2y + 2y2 + -3y2 = -18 + -2y + 3y2 + 18 + 2y + -3y2

Combine like terms: 5y + 2y = 7y
18 + 7y + 2y2 + -3y2 = -18 + -2y + 3y2 + 18 + 2y + -3y2

Combine like terms: 2y2 + -3y2 = -1y2
18 + 7y + -1y2 = -18 + -2y + 3y2 + 18 + 2y + -3y2

Reorder the terms:
18 + 7y + -1y2 = -18 + 18 + -2y + 2y + 3y2 + -3y2

Combine like terms: -18 + 18 = 0
18 + 7y + -1y2 = 0 + -2y + 2y + 3y2 + -3y2
18 + 7y + -1y2 = -2y + 2y + 3y2 + -3y2

Combine like terms: -2y + 2y = 0
18 + 7y + -1y2 = 0 + 3y2 + -3y2
18 + 7y + -1y2 = 3y2 + -3y2

Combine like terms: 3y2 + -3y2 = 0
18 + 7y + -1y2 = 0

Factor a trinomial.
(9 + -1y)(2 + y) = 0


Subproblem 1
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9

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

Simplifying
2 + y = 0

Solving
2 + y = 0

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

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

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

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

Simplifying
y = -2
Solution
y = {9, -2}

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