(2y+1)(3+y)=0

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Solution for (2y+1)(3+y)=0 equation:


Simplifying
(2y + 1)(3 + y) = 0

Reorder the terms:
(1 + 2y)(3 + y) = 0

Multiply (1 + 2y) * (3 + y)
(1(3 + y) + 2y * (3 + y)) = 0
((3 * 1 + y * 1) + 2y * (3 + y)) = 0
((3 + 1y) + 2y * (3 + y)) = 0
(3 + 1y + (3 * 2y + y * 2y)) = 0
(3 + 1y + (6y + 2y2)) = 0

Combine like terms: 1y + 6y = 7y
(3 + 7y + 2y2) = 0

Solving
3 + 7y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + y)(1 + 2y) = 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 '(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

Solution

y = {-3, -0.5}

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