y^2+2y-10=4y-2

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Solution for y^2+2y-10=4y-2 equation: 


Simplifying
y2 + 2y + -10 = 4y + -2

Reorder the terms:
-10 + 2y + y2 = 4y + -2

Reorder the terms:
-10 + 2y + y2 = -2 + 4y

Solving
-10 + 2y + y2 = -2 + 4y

Solving for variable 'y'.

Reorder the terms:
-10 + 2 + 2y + -4y + y2 = -2 + 4y + 2 + -4y

Combine like terms: -10 + 2 = -8
-8 + 2y + -4y + y2 = -2 + 4y + 2 + -4y

Combine like terms: 2y + -4y = -2y
-8 + -2y + y2 = -2 + 4y + 2 + -4y

Reorder the terms:
-8 + -2y + y2 = -2 + 2 + 4y + -4y

Combine like terms: -2 + 2 = 0
-8 + -2y + y2 = 0 + 4y + -4y
-8 + -2y + y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-8 + -2y + y2 = 0

Factor a trinomial.
(-2 + -1y)(4 + -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 '(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 = {-2, 4}

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