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

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


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

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

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

Multiply (-4 + 3y) * (-1 + 4y)
(-4(-1 + 4y) + 3y * (-1 + 4y)) = 0
((-1 * -4 + 4y * -4) + 3y * (-1 + 4y)) = 0
((4 + -16y) + 3y * (-1 + 4y)) = 0
(4 + -16y + (-1 * 3y + 4y * 3y)) = 0
(4 + -16y + (-3y + 12y2)) = 0

Combine like terms: -16y + -3y = -19y
(4 + -19y + 12y2) = 0

Solving
4 + -19y + 12y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + -4y)(4 + -3y) = 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 '(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 = {0.25, 1.333333333}

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