y^2+2y-6=-y+4

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Solution for y^2+2y-6=-y+4 equation:


Simplifying
y2 + 2y + -6 = -1y + 4

Reorder the terms:
-6 + 2y + y2 = -1y + 4

Reorder the terms:
-6 + 2y + y2 = 4 + -1y

Solving
-6 + 2y + y2 = 4 + -1y

Solving for variable 'y'.

Reorder the terms:
-6 + -4 + 2y + y + y2 = 4 + -1y + -4 + y

Combine like terms: -6 + -4 = -10
-10 + 2y + y + y2 = 4 + -1y + -4 + y

Combine like terms: 2y + y = 3y
-10 + 3y + y2 = 4 + -1y + -4 + y

Reorder the terms:
-10 + 3y + y2 = 4 + -4 + -1y + y

Combine like terms: 4 + -4 = 0
-10 + 3y + y2 = 0 + -1y + y
-10 + 3y + y2 = -1y + y

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

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

Solution

y = {-5, 2}

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