(8y-3)(4y+1)=0

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Solution for (8y-3)(4y+1)=0 equation:


Simplifying
(8y + -3)(4y + 1) = 0

Reorder the terms:
(-3 + 8y)(4y + 1) = 0

Reorder the terms:
(-3 + 8y)(1 + 4y) = 0

Multiply (-3 + 8y) * (1 + 4y)
(-3(1 + 4y) + 8y * (1 + 4y)) = 0
((1 * -3 + 4y * -3) + 8y * (1 + 4y)) = 0
((-3 + -12y) + 8y * (1 + 4y)) = 0
(-3 + -12y + (1 * 8y + 4y * 8y)) = 0
(-3 + -12y + (8y + 32y2)) = 0

Combine like terms: -12y + 8y = -4y
(-3 + -4y + 32y2) = 0

Solving
-3 + -4y + 32y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -4y)(3 + -8y) = 0

Subproblem 1

Set the factor '(-1 + -4y)' equal to zero and attempt to solve: Simplifying -1 + -4y = 0 Solving -1 + -4y = 0 Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4y = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4y = 0 + 1 -4y = 0 + 1 Combine like terms: 0 + 1 = 1 -4y = 1 Divide each side by '-4'. y = -0.25 Simplifying y = -0.25

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 = {-0.25, 0.375}

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