(3y-12)(4y+8)=0

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Solution for (3y-12)(4y+8)=0 equation:


Simplifying
(3y + -12)(4y + 8) = 0

Reorder the terms:
(-12 + 3y)(4y + 8) = 0

Reorder the terms:
(-12 + 3y)(8 + 4y) = 0

Multiply (-12 + 3y) * (8 + 4y)
(-12(8 + 4y) + 3y * (8 + 4y)) = 0
((8 * -12 + 4y * -12) + 3y * (8 + 4y)) = 0
((-96 + -48y) + 3y * (8 + 4y)) = 0
(-96 + -48y + (8 * 3y + 4y * 3y)) = 0
(-96 + -48y + (24y + 12y2)) = 0

Combine like terms: -48y + 24y = -24y
(-96 + -24y + 12y2) = 0

Solving
-96 + -24y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '12'.
12(-8 + -2y + y2) = 0

Factor a trinomial.
12((-2 + -1y)(4 + -1y)) = 0

Ignore the factor 12.

Subproblem 1
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

Subproblem 2
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
Solution
y = {-2, 4}

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