y^2+3y-10=2y+10

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Solution for y^2+3y-10=2y+10 equation: 


Simplifying
y2 + 3y + -10 = 2y + 10

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

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

Solving
-10 + 3y + y2 = 10 + 2y

Solving for variable 'y'.

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

Combine like terms: -10 + -10 = -20
-20 + 3y + -2y + y2 = 10 + 2y + -10 + -2y

Combine like terms: 3y + -2y = 1y
-20 + 1y + y2 = 10 + 2y + -10 + -2y

Reorder the terms:
-20 + 1y + y2 = 10 + -10 + 2y + -2y

Combine like terms: 10 + -10 = 0
-20 + 1y + y2 = 0 + 2y + -2y
-20 + 1y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
-20 + 1y + y2 = 0

Factor a trinomial.
(-5 + -1y)(4 + -1y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {-5, 4}

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