(5y+7)(2+y)=0

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Solution for (5y+7)(2+y)=0 equation:


Simplifying
(5y + 7)(2 + y) = 0

Reorder the terms:
(7 + 5y)(2 + y) = 0

Multiply (7 + 5y) * (2 + y)
(7(2 + y) + 5y * (2 + y)) = 0
((2 * 7 + y * 7) + 5y * (2 + y)) = 0
((14 + 7y) + 5y * (2 + y)) = 0
(14 + 7y + (2 * 5y + y * 5y)) = 0
(14 + 7y + (10y + 5y2)) = 0

Combine like terms: 7y + 10y = 17y
(14 + 17y + 5y2) = 0

Solving
14 + 17y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + y)(7 + 5y) = 0

Subproblem 1

Set the factor '(2 + y)' equal to zero and attempt to solve: Simplifying 2 + y = 0 Solving 2 + y = 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 + y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + y = 0 + -2 y = 0 + -2 Combine like terms: 0 + -2 = -2 y = -2 Simplifying y = -2

Subproblem 2

Set the factor '(7 + 5y)' equal to zero and attempt to solve: Simplifying 7 + 5y = 0 Solving 7 + 5y = 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 + 5y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 5y = 0 + -7 5y = 0 + -7 Combine like terms: 0 + -7 = -7 5y = -7 Divide each side by '5'. y = -1.4 Simplifying y = -1.4

Solution

y = {-2, -1.4}

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