(y+4)(3y-6)=0

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Solution for (y+4)(3y-6)=0 equation:


Simplifying
(y + 4)(3y + -6) = 0

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

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

Multiply (4 + y) * (-6 + 3y)
(4(-6 + 3y) + y(-6 + 3y)) = 0
((-6 * 4 + 3y * 4) + y(-6 + 3y)) = 0
((-24 + 12y) + y(-6 + 3y)) = 0
(-24 + 12y + (-6 * y + 3y * y)) = 0
(-24 + 12y + (-6y + 3y2)) = 0

Combine like terms: 12y + -6y = 6y
(-24 + 6y + 3y2) = 0

Solving
-24 + 6y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 2y + y2) = 0

Factor a trinomial.
3((-4 + -1y)(2 + -1y)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + -1y)' equal to zero and attempt to solve: Simplifying -4 + -1y = 0 Solving -4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1y = 0 + 4 -1y = 0 + 4 Combine like terms: 0 + 4 = 4 -1y = 4 Divide each side by '-1'. y = -4 Simplifying y = -4

Subproblem 2

Set the factor '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 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 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2

Solution

y = {-4, 2}

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