2y^2-15-5y=y^2-3y

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Solution for 2y^2-15-5y=y^2-3y equation: 


Simplifying
2y2 + -15 + -5y = y2 + -3y

Reorder the terms:
-15 + -5y + 2y2 = y2 + -3y

Reorder the terms:
-15 + -5y + 2y2 = -3y + y2

Solving
-15 + -5y + 2y2 = -3y + y2

Solving for variable 'y'.

Reorder the terms:
-15 + -5y + 3y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2

Combine like terms: -5y + 3y = -2y
-15 + -2y + 2y2 + -1y2 = -3y + y2 + 3y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-15 + -2y + 1y2 = -3y + y2 + 3y + -1y2

Reorder the terms:
-15 + -2y + 1y2 = -3y + 3y + y2 + -1y2

Combine like terms: -3y + 3y = 0
-15 + -2y + 1y2 = 0 + y2 + -1y2
-15 + -2y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-15 + -2y + 1y2 = 0

Factor a trinomial.
(-3 + -1y)(5 + -1y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-3, 5}

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