9=2y(4y-3)

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Solution for 9=2y(4y-3) equation:


Simplifying
9 = 2y(4y + -3)

Reorder the terms:
9 = 2y(-3 + 4y)
9 = (-3 * 2y + 4y * 2y)
9 = (-6y + 8y2)

Solving
9 = -6y + 8y2

Solving for variable 'y'.

Reorder the terms:
9 + 6y + -8y2 = -6y + 6y + 8y2 + -8y2

Combine like terms: -6y + 6y = 0
9 + 6y + -8y2 = 0 + 8y2 + -8y2
9 + 6y + -8y2 = 8y2 + -8y2

Combine like terms: 8y2 + -8y2 = 0
9 + 6y + -8y2 = 0

Factor a trinomial.
(3 + -2y)(3 + 4y) = 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 + 4y)' equal to zero and attempt to solve: Simplifying 3 + 4y = 0 Solving 3 + 4y = 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 + 4y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4y = 0 + -3 4y = 0 + -3 Combine like terms: 0 + -3 = -3 4y = -3 Divide each side by '4'. y = -0.75 Simplifying y = -0.75

Solution

y = {1.5, -0.75}

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