2y(4y+3)=9

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


Simplifying
2y(4y + 3) = 9

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

Solving
6y + 8y2 = 9

Solving for variable 'y'.

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

Combine like terms: 9 + -9 = 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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