3y(y+5)=42

Solution for 3y(y+5)=42 equation:

Simplifying
3y(y + 5) = 42

Reorder the terms:
3y(5 + y) = 42
(5 * 3y + y * 3y) = 42
(15y + 3y2) = 42

Solving
15y + 3y2 = 42

Solving for variable 'y'.

Reorder the terms:
-42 + 15y + 3y2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 15y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5y + y2) = 0

Factor a trinomial.
3((-7 + -1y)(2 + -1y)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(2 + -1y)' equal to zero and attempt to solve:

Simplifying
2 + -1y = 0

Solving
2 + -1y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y = 0 + -2
-1y = 0 + -2

Combine like terms: 0 + -2 = -2
-1y = -2

Divide each side by '-1'.
y = 2

Simplifying
y = 2
Solution
y = {-7, 2}