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

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


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

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

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

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

Combine like terms: 15y + -2y = 13y
(-5 + 13y + 6y2) = 0

Solving
-5 + 13y + 6y2 = 0

Solving for variable 'y'.

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

Subproblem 1

Set the factor '(-5 + -2y)' equal to zero and attempt to solve: Simplifying -5 + -2y = 0 Solving -5 + -2y = 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 + -2y = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2y = 0 + 5 -2y = 0 + 5 Combine like terms: 0 + 5 = 5 -2y = 5 Divide each side by '-2'. y = -2.5 Simplifying y = -2.5

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 = {-2.5, 0.3333333333}

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