3y(5y+14)=9

Solution for 3y(5y+14)=9 equation:

Simplifying
3y(5y + 14) = 9

Reorder the terms:
3y(14 + 5y) = 9
(14 * 3y + 5y * 3y) = 9
(42y + 15y2) = 9

Solving
42y + 15y2 = 9

Solving for variable 'y'.

Reorder the terms:
-9 + 42y + 15y2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 42y + 15y2 = 0

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

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

Ignore the factor 3.
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 '(1 + -5y)' equal to zero and attempt to solve:

Simplifying
1 + -5y = 0

Solving
1 + -5y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5y = 0 + -1
-5y = 0 + -1

Combine like terms: 0 + -1 = -1
-5y = -1

Divide each side by '-5'.
y = 0.2

Simplifying
y = 0.2
Solution
y = {-3, 0.2}