132y+32y^2-54=0

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Solution for 132y+32y^2-54=0 equation:


Simplifying
132y + 32y2 + -54 = 0

Reorder the terms:
-54 + 132y + 32y2 = 0

Solving
-54 + 132y + 32y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + 66y + 16y2) = 0

Factor a trinomial.
2((-9 + -2y)(3 + -8y)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-9 + -2y)' equal to zero and attempt to solve: Simplifying -9 + -2y = 0 Solving -9 + -2y = 0 Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2y = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2y = 0 + 9 -2y = 0 + 9 Combine like terms: 0 + 9 = 9 -2y = 9 Divide each side by '-2'. y = -4.5 Simplifying y = -4.5

Subproblem 2

Set the factor '(3 + -8y)' equal to zero and attempt to solve: Simplifying 3 + -8y = 0 Solving 3 + -8y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -8y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8y = 0 + -3 -8y = 0 + -3 Combine like terms: 0 + -3 = -3 -8y = -3 Divide each side by '-8'. y = 0.375 Simplifying y = 0.375

Solution

y = {-4.5, 0.375}

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