5y(y+3)=4y+12

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Solution for 5y(y+3)=4y+12 equation:


Simplifying
5y(y + 3) = 4y + 12

Reorder the terms:
5y(3 + y) = 4y + 12
(3 * 5y + y * 5y) = 4y + 12
(15y + 5y2) = 4y + 12

Reorder the terms:
15y + 5y2 = 12 + 4y

Solving
15y + 5y2 = 12 + 4y

Solving for variable 'y'.

Reorder the terms:
-12 + 15y + -4y + 5y2 = 12 + 4y + -12 + -4y

Combine like terms: 15y + -4y = 11y
-12 + 11y + 5y2 = 12 + 4y + -12 + -4y

Reorder the terms:
-12 + 11y + 5y2 = 12 + -12 + 4y + -4y

Combine like terms: 12 + -12 = 0
-12 + 11y + 5y2 = 0 + 4y + -4y
-12 + 11y + 5y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
-12 + 11y + 5y2 = 0

Factor a trinomial.
(-3 + -1y)(4 + -5y) = 0

Subproblem 1

Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 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 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3

Subproblem 2

Set the factor '(4 + -5y)' equal to zero and attempt to solve: Simplifying 4 + -5y = 0 Solving 4 + -5y = 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 + -5y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5y = 0 + -4 -5y = 0 + -4 Combine like terms: 0 + -4 = -4 -5y = -4 Divide each side by '-5'. y = 0.8 Simplifying y = 0.8

Solution

y = {-3, 0.8}

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