y^2+5y-10=4y+2

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Solution for y^2+5y-10=4y+2 equation: 


Simplifying
y2 + 5y + -10 = 4y + 2

Reorder the terms:
-10 + 5y + y2 = 4y + 2

Reorder the terms:
-10 + 5y + y2 = 2 + 4y

Solving
-10 + 5y + y2 = 2 + 4y

Solving for variable 'y'.

Reorder the terms:
-10 + -2 + 5y + -4y + y2 = 2 + 4y + -2 + -4y

Combine like terms: -10 + -2 = -12
-12 + 5y + -4y + y2 = 2 + 4y + -2 + -4y

Combine like terms: 5y + -4y = 1y
-12 + 1y + y2 = 2 + 4y + -2 + -4y

Reorder the terms:
-12 + 1y + y2 = 2 + -2 + 4y + -4y

Combine like terms: 2 + -2 = 0
-12 + 1y + y2 = 0 + 4y + -4y
-12 + 1y + y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-12 + 1y + y2 = 0

Factor a trinomial.
(-4 + -1y)(3 + -1y) = 0


Subproblem 1
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

Subproblem 2
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
Solution
y = {-4, 3}

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