12y^2+8y-32=0

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Solution for 12y^2+8y-32=0 equation:


Simplifying
12y2 + 8y + -32 = 0

Reorder the terms:
-32 + 8y + 12y2 = 0

Solving
-32 + 8y + 12y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 2y + 3y2) = 0

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

Ignore the factor 4.

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 + -3y)' equal to zero and attempt to solve: Simplifying 4 + -3y = 0 Solving 4 + -3y = 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 + -3y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3y = 0 + -4 -3y = 0 + -4 Combine like terms: 0 + -4 = -4 -3y = -4 Divide each side by '-3'. y = 1.333333333 Simplifying y = 1.333333333

Solution

y = {-2, 1.333333333}

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