32y+48=3y^2

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Solution for 32y+48=3y^2 equation:


Simplifying
32y + 48 = 3y2

Reorder the terms:
48 + 32y = 3y2

Solving
48 + 32y = 3y2

Solving for variable 'y'.

Combine like terms: 3y2 + -3y2 = 0
48 + 32y + -3y2 = 0

Factor a trinomial.
(12 + -1y)(4 + 3y) = 0

Subproblem 1

Set the factor '(12 + -1y)' equal to zero and attempt to solve: Simplifying 12 + -1y = 0 Solving 12 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1y = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1y = 0 + -12 -1y = 0 + -12 Combine like terms: 0 + -12 = -12 -1y = -12 Divide each side by '-1'. y = 12 Simplifying y = 12

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 = {12, -1.333333333}

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