(4y+1)(2y-3)=0

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Solution for (4y+1)(2y-3)=0 equation:


Simplifying
(4y + 1)(2y + -3) = 0

Reorder the terms:
(1 + 4y)(2y + -3) = 0

Reorder the terms:
(1 + 4y)(-3 + 2y) = 0

Multiply (1 + 4y) * (-3 + 2y)
(1(-3 + 2y) + 4y * (-3 + 2y)) = 0
((-3 * 1 + 2y * 1) + 4y * (-3 + 2y)) = 0
((-3 + 2y) + 4y * (-3 + 2y)) = 0
(-3 + 2y + (-3 * 4y + 2y * 4y)) = 0
(-3 + 2y + (-12y + 8y2)) = 0

Combine like terms: 2y + -12y = -10y
(-3 + -10y + 8y2) = 0

Solving
-3 + -10y + 8y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -4y)(3 + -2y) = 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 + -2y)' equal to zero and attempt to solve: Simplifying 3 + -2y = 0 Solving 3 + -2y = 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 + -2y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2y = 0 + -3 -2y = 0 + -3 Combine like terms: 0 + -3 = -3 -2y = -3 Divide each side by '-2'. y = 1.5 Simplifying y = 1.5

Solution

y = {-0.25, 1.5}

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