2y^2-10-5y=y^2-2y

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Solution for 2y^2-10-5y=y^2-2y equation: 


Simplifying
2y2 + -10 + -5y = y2 + -2y

Reorder the terms:
-10 + -5y + 2y2 = y2 + -2y

Reorder the terms:
-10 + -5y + 2y2 = -2y + y2

Solving
-10 + -5y + 2y2 = -2y + y2

Solving for variable 'y'.

Reorder the terms:
-10 + -5y + 2y + 2y2 + -1y2 = -2y + y2 + 2y + -1y2

Combine like terms: -5y + 2y = -3y
-10 + -3y + 2y2 + -1y2 = -2y + y2 + 2y + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-10 + -3y + 1y2 = -2y + y2 + 2y + -1y2

Reorder the terms:
-10 + -3y + 1y2 = -2y + 2y + y2 + -1y2

Combine like terms: -2y + 2y = 0
-10 + -3y + 1y2 = 0 + y2 + -1y2
-10 + -3y + 1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-10 + -3y + 1y2 = 0

Factor a trinomial.
(-2 + -1y)(5 + -1y) = 0


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

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

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

Divide each side by '-1'.
y = -2

Simplifying
y = -2

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 = {-2, 5}

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