(7y-1)(2y+3)=0

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Solution for (7y-1)(2y+3)=0 equation:


Simplifying
(7y + -1)(2y + 3) = 0

Reorder the terms:
(-1 + 7y)(2y + 3) = 0

Reorder the terms:
(-1 + 7y)(3 + 2y) = 0

Multiply (-1 + 7y) * (3 + 2y)
(-1(3 + 2y) + 7y * (3 + 2y)) = 0
((3 * -1 + 2y * -1) + 7y * (3 + 2y)) = 0
((-3 + -2y) + 7y * (3 + 2y)) = 0
(-3 + -2y + (3 * 7y + 2y * 7y)) = 0
(-3 + -2y + (21y + 14y2)) = 0

Combine like terms: -2y + 21y = 19y
(-3 + 19y + 14y2) = 0

Solving
-3 + 19y + 14y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-3 + -2y)(1 + -7y) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(1 + -7y)' equal to zero and attempt to solve: Simplifying 1 + -7y = 0 Solving 1 + -7y = 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 + -7y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7y = 0 + -1 -7y = 0 + -1 Combine like terms: 0 + -1 = -1 -7y = -1 Divide each side by '-7'. y = 0.1428571429 Simplifying y = 0.1428571429

Solution

y = {-1.5, 0.1428571429}

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