(5y-2)(9+y)=0

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Solution for (5y-2)(9+y)=0 equation:


Simplifying
(5y + -2)(9 + y) = 0

Reorder the terms:
(-2 + 5y)(9 + y) = 0

Multiply (-2 + 5y) * (9 + y)
(-2(9 + y) + 5y * (9 + y)) = 0
((9 * -2 + y * -2) + 5y * (9 + y)) = 0
((-18 + -2y) + 5y * (9 + y)) = 0
(-18 + -2y + (9 * 5y + y * 5y)) = 0
(-18 + -2y + (45y + 5y2)) = 0

Combine like terms: -2y + 45y = 43y
(-18 + 43y + 5y2) = 0

Solving
-18 + 43y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-9 + -1y)(2 + -5y) = 0

Subproblem 1

Set the factor '(-9 + -1y)' equal to zero and attempt to solve: Simplifying -9 + -1y = 0 Solving -9 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1y = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1y = 0 + 9 -1y = 0 + 9 Combine like terms: 0 + 9 = 9 -1y = 9 Divide each side by '-1'. y = -9 Simplifying y = -9

Subproblem 2

Set the factor '(2 + -5y)' equal to zero and attempt to solve: Simplifying 2 + -5y = 0 Solving 2 + -5y = 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 + -5y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5y = 0 + -2 -5y = 0 + -2 Combine like terms: 0 + -2 = -2 -5y = -2 Divide each side by '-5'. y = 0.4 Simplifying y = 0.4

Solution

y = {-9, 0.4}

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