48y^2+120y+75=0

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Solution for 48y^2+120y+75=0 equation:


Simplifying
48y2 + 120y + 75 = 0

Reorder the terms:
75 + 120y + 48y2 = 0

Solving
75 + 120y + 48y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + 40y + 16y2) = 0

Factor a trinomial.
3((5 + 4y)(5 + 4y)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(5 + 4y)' equal to zero and attempt to solve: Simplifying 5 + 4y = 0 Solving 5 + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4y = 0 + -5 4y = 0 + -5 Combine like terms: 0 + -5 = -5 4y = -5 Divide each side by '4'. y = -1.25 Simplifying y = -1.25

Subproblem 2

Set the factor '(5 + 4y)' equal to zero and attempt to solve: Simplifying 5 + 4y = 0 Solving 5 + 4y = 0 Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4y = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4y = 0 + -5 4y = 0 + -5 Combine like terms: 0 + -5 = -5 4y = -5 Divide each side by '4'. y = -1.25 Simplifying y = -1.25

Solution

y = {-1.25, -1.25}

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