5y(y+3)=6(y+3)

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Solution for 5y(y+3)=6(y+3) equation: 


Simplifying
5y(y + 3) = 6(y + 3)

Reorder the terms:
5y(3 + y) = 6(y + 3)
(3 * 5y + y * 5y) = 6(y + 3)
(15y + 5y2) = 6(y + 3)

Reorder the terms:
15y + 5y2 = 6(3 + y)
15y + 5y2 = (3 * 6 + y * 6)
15y + 5y2 = (18 + 6y)

Solving
15y + 5y2 = 18 + 6y

Solving for variable 'y'.

Reorder the terms:
-18 + 15y + -6y + 5y2 = 18 + 6y + -18 + -6y

Combine like terms: 15y + -6y = 9y
-18 + 9y + 5y2 = 18 + 6y + -18 + -6y

Reorder the terms:
-18 + 9y + 5y2 = 18 + -18 + 6y + -6y

Combine like terms: 18 + -18 = 0
-18 + 9y + 5y2 = 0 + 6y + -6y
-18 + 9y + 5y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
-18 + 9y + 5y2 = 0

Factor a trinomial.
(-3 + -1y)(6 + -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 '(6 + -5y)' equal to zero and attempt to solve:

Simplifying
6 + -5y = 0

Solving
6 + -5y = 0

Move all terms containing y to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5y = 0 + -6
-5y = 0 + -6

Combine like terms: 0 + -6 = -6
-5y = -6

Divide each side by '-5'.
y = 1.2

Simplifying
y = 1.2
Solution
y = {-3, 1.2}

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