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

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Solution for (6-y)(3y+5)=0 equation:


Simplifying
(6 + -1y)(3y + 5) = 0

Reorder the terms:
(6 + -1y)(5 + 3y) = 0

Multiply (6 + -1y) * (5 + 3y)
(6(5 + 3y) + -1y * (5 + 3y)) = 0
((5 * 6 + 3y * 6) + -1y * (5 + 3y)) = 0
((30 + 18y) + -1y * (5 + 3y)) = 0
(30 + 18y + (5 * -1y + 3y * -1y)) = 0
(30 + 18y + (-5y + -3y2)) = 0

Combine like terms: 18y + -5y = 13y
(30 + 13y + -3y2) = 0

Solving
30 + 13y + -3y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + -1y)(5 + 3y) = 0

Subproblem 1

Set the factor '(6 + -1y)' equal to zero and attempt to solve: Simplifying 6 + -1y = 0 Solving 6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1y = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1y = 0 + -6 -1y = 0 + -6 Combine like terms: 0 + -6 = -6 -1y = -6 Divide each side by '-1'. y = 6 Simplifying y = 6

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 = {6, -1.666666667}

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