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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