(3y+5)(3+y)=0

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Solution for (3y+5)(3+y)=0 equation:


Simplifying
(3y + 5)(3 + y) = 0

Reorder the terms:
(5 + 3y)(3 + y) = 0

Multiply (5 + 3y) * (3 + y)
(5(3 + y) + 3y * (3 + y)) = 0
((3 * 5 + y * 5) + 3y * (3 + y)) = 0
((15 + 5y) + 3y * (3 + y)) = 0
(15 + 5y + (3 * 3y + y * 3y)) = 0
(15 + 5y + (9y + 3y2)) = 0

Combine like terms: 5y + 9y = 14y
(15 + 14y + 3y2) = 0

Solving
15 + 14y + 3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + y)(5 + 3y) = 0

Subproblem 1

Set the factor '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3

Subproblem 2

Set the factor '(5 + 3y)' equal to zero and attempt to solve: Simplifying 5 + 3y = 0 Solving 5 + 3y = 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 + 3y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3y = 0 + -5 3y = 0 + -5 Combine like terms: 0 + -5 = -5 3y = -5 Divide each side by '3'. y = -1.666666667 Simplifying y = -1.666666667

Solution

y = {-3, -1.666666667}

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