Y^2+9Y=8Y+56

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Solution for Y^2+9Y=8Y+56 equation:


Simplifying
Y2 + 9Y = 8Y + 56

Reorder the terms:
9Y + Y2 = 8Y + 56

Reorder the terms:
9Y + Y2 = 56 + 8Y

Solving
9Y + Y2 = 56 + 8Y

Solving for variable 'Y'.

Reorder the terms:
-56 + 9Y + -8Y + Y2 = 56 + 8Y + -56 + -8Y

Combine like terms: 9Y + -8Y = 1Y
-56 + 1Y + Y2 = 56 + 8Y + -56 + -8Y

Reorder the terms:
-56 + 1Y + Y2 = 56 + -56 + 8Y + -8Y

Combine like terms: 56 + -56 = 0
-56 + 1Y + Y2 = 0 + 8Y + -8Y
-56 + 1Y + Y2 = 8Y + -8Y

Combine like terms: 8Y + -8Y = 0
-56 + 1Y + Y2 = 0

Factor a trinomial.
(-8 + -1Y)(7 + -1Y) = 0

Subproblem 1

Set the factor '(-8 + -1Y)' equal to zero and attempt to solve: Simplifying -8 + -1Y = 0 Solving -8 + -1Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1Y = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1Y = 0 + 8 -1Y = 0 + 8 Combine like terms: 0 + 8 = 8 -1Y = 8 Divide each side by '-1'. Y = -8 Simplifying Y = -8

Subproblem 2

Set the factor '(7 + -1Y)' equal to zero and attempt to solve: Simplifying 7 + -1Y = 0 Solving 7 + -1Y = 0 Move all terms containing Y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1Y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1Y = 0 + -7 -1Y = 0 + -7 Combine like terms: 0 + -7 = -7 -1Y = -7 Divide each side by '-1'. Y = 7 Simplifying Y = 7

Solution

Y = {-8, 7}

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