(Y+7)(Y-5)=0

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Solution for (Y+7)(Y-5)=0 equation:


Simplifying
(Y + 7)(Y + -5) = 0

Reorder the terms:
(7 + Y)(Y + -5) = 0

Reorder the terms:
(7 + Y)(-5 + Y) = 0

Multiply (7 + Y) * (-5 + Y)
(7(-5 + Y) + Y(-5 + Y)) = 0
((-5 * 7 + Y * 7) + Y(-5 + Y)) = 0
((-35 + 7Y) + Y(-5 + Y)) = 0
(-35 + 7Y + (-5 * Y + Y * Y)) = 0
(-35 + 7Y + (-5Y + Y2)) = 0

Combine like terms: 7Y + -5Y = 2Y
(-35 + 2Y + Y2) = 0

Solving
-35 + 2Y + Y2 = 0

Solving for variable 'Y'.

Factor a trinomial.
(-7 + -1Y)(5 + -1Y) = 0

Subproblem 1

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

Subproblem 2

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

Solution

Y = {-7, 5}

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