y^2-7y-7=-3y+5

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Solution for y^2-7y-7=-3y+5 equation:


Simplifying
y2 + -7y + -7 = -3y + 5

Reorder the terms:
-7 + -7y + y2 = -3y + 5

Reorder the terms:
-7 + -7y + y2 = 5 + -3y

Solving
-7 + -7y + y2 = 5 + -3y

Solving for variable 'y'.

Reorder the terms:
-7 + -5 + -7y + 3y + y2 = 5 + -3y + -5 + 3y

Combine like terms: -7 + -5 = -12
-12 + -7y + 3y + y2 = 5 + -3y + -5 + 3y

Combine like terms: -7y + 3y = -4y
-12 + -4y + y2 = 5 + -3y + -5 + 3y

Reorder the terms:
-12 + -4y + y2 = 5 + -5 + -3y + 3y

Combine like terms: 5 + -5 = 0
-12 + -4y + y2 = 0 + -3y + 3y
-12 + -4y + y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
-12 + -4y + y2 = 0

Factor a trinomial.
(-2 + -1y)(6 + -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 '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6

Solution

y = {-2, 6}

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