(3y+1)(5y+2)=0

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Solution for (3y+1)(5y+2)=0 equation:


Simplifying
(3y + 1)(5y + 2) = 0

Reorder the terms:
(1 + 3y)(5y + 2) = 0

Reorder the terms:
(1 + 3y)(2 + 5y) = 0

Multiply (1 + 3y) * (2 + 5y)
(1(2 + 5y) + 3y * (2 + 5y)) = 0
((2 * 1 + 5y * 1) + 3y * (2 + 5y)) = 0
((2 + 5y) + 3y * (2 + 5y)) = 0
(2 + 5y + (2 * 3y + 5y * 3y)) = 0
(2 + 5y + (6y + 15y2)) = 0

Combine like terms: 5y + 6y = 11y
(2 + 11y + 15y2) = 0

Solving
2 + 11y + 15y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + 5y)(1 + 3y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + 3y)' equal to zero and attempt to solve: Simplifying 1 + 3y = 0 Solving 1 + 3y = 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 + 3y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3y = 0 + -1 3y = 0 + -1 Combine like terms: 0 + -1 = -1 3y = -1 Divide each side by '3'. y = -0.3333333333 Simplifying y = -0.3333333333

Solution

y = {-0.4, -0.3333333333}

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