(2y-7)(2y-3)=4(-8y+3)

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Solution for (2y-7)(2y-3)=4(-8y+3) equation:


Simplifying
(2y + -7)(2y + -3) = 4(-8y + 3)

Reorder the terms:
(-7 + 2y)(2y + -3) = 4(-8y + 3)

Reorder the terms:
(-7 + 2y)(-3 + 2y) = 4(-8y + 3)

Multiply (-7 + 2y) * (-3 + 2y)
(-7(-3 + 2y) + 2y * (-3 + 2y)) = 4(-8y + 3)
((-3 * -7 + 2y * -7) + 2y * (-3 + 2y)) = 4(-8y + 3)
((21 + -14y) + 2y * (-3 + 2y)) = 4(-8y + 3)
(21 + -14y + (-3 * 2y + 2y * 2y)) = 4(-8y + 3)
(21 + -14y + (-6y + 4y2)) = 4(-8y + 3)

Combine like terms: -14y + -6y = -20y
(21 + -20y + 4y2) = 4(-8y + 3)

Reorder the terms:
21 + -20y + 4y2 = 4(3 + -8y)
21 + -20y + 4y2 = (3 * 4 + -8y * 4)
21 + -20y + 4y2 = (12 + -32y)

Solving
21 + -20y + 4y2 = 12 + -32y

Solving for variable 'y'.

Reorder the terms:
21 + -12 + -20y + 32y + 4y2 = 12 + -32y + -12 + 32y

Combine like terms: 21 + -12 = 9
9 + -20y + 32y + 4y2 = 12 + -32y + -12 + 32y

Combine like terms: -20y + 32y = 12y
9 + 12y + 4y2 = 12 + -32y + -12 + 32y

Reorder the terms:
9 + 12y + 4y2 = 12 + -12 + -32y + 32y

Combine like terms: 12 + -12 = 0
9 + 12y + 4y2 = 0 + -32y + 32y
9 + 12y + 4y2 = -32y + 32y

Combine like terms: -32y + 32y = 0
9 + 12y + 4y2 = 0

Factor a trinomial.
(3 + 2y)(3 + 2y) = 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 '(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 = {-1.5, -1.5}

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