(-2y+1)(y+5)=0

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Solution for (-2y+1)(y+5)=0 equation:


Simplifying
(-2y + 1)(y + 5) = 0

Reorder the terms:
(1 + -2y)(y + 5) = 0

Reorder the terms:
(1 + -2y)(5 + y) = 0

Multiply (1 + -2y) * (5 + y)
(1(5 + y) + -2y * (5 + y)) = 0
((5 * 1 + y * 1) + -2y * (5 + y)) = 0
((5 + 1y) + -2y * (5 + y)) = 0
(5 + 1y + (5 * -2y + y * -2y)) = 0
(5 + 1y + (-10y + -2y2)) = 0

Combine like terms: 1y + -10y = -9y
(5 + -9y + -2y2) = 0

Solving
5 + -9y + -2y2 = 0

Solving for variable 'y'.

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

Subproblem 1

Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Divide each side by '-2'. y = 0.5 Simplifying y = 0.5

Subproblem 2

Set the factor '(5 + y)' equal to zero and attempt to solve: Simplifying 5 + y = 0 Solving 5 + y = 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 + y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + y = 0 + -5 y = 0 + -5 Combine like terms: 0 + -5 = -5 y = -5 Simplifying y = -5

Solution

y = {0.5, -5}

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