y(2y+5)=12

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Solution for y(2y+5)=12 equation:


Simplifying
y(2y + 5) = 12

Reorder the terms:
y(5 + 2y) = 12
(5 * y + 2y * y) = 12
(5y + 2y2) = 12

Solving
5y + 2y2 = 12

Solving for variable 'y'.

Reorder the terms:
-12 + 5y + 2y2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 5y + 2y2 = 0

Factor a trinomial.
(-4 + -1y)(3 + -2y) = 0

Subproblem 1

Set the factor '(-4 + -1y)' equal to zero and attempt to solve: Simplifying -4 + -1y = 0 Solving -4 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1y = 0 + 4 -1y = 0 + 4 Combine like terms: 0 + 4 = 4 -1y = 4 Divide each side by '-1'. y = -4 Simplifying y = -4

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 = {-4, 1.5}

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