(6y+3)(10y+12)=

Solution for (6y+3)(10y+12)= equation:

Simplifying
(6y + 3)(10y + 12) = 0

Reorder the terms:
(3 + 6y)(10y + 12) = 0

Reorder the terms:
(3 + 6y)(12 + 10y) = 0

Multiply (3 + 6y) * (12 + 10y)
(3(12 + 10y) + 6y * (12 + 10y)) = 0
((12 * 3 + 10y * 3) + 6y * (12 + 10y)) = 0
((36 + 30y) + 6y * (12 + 10y)) = 0
(36 + 30y + (12 * 6y + 10y * 6y)) = 0
(36 + 30y + (72y + 60y2)) = 0

Combine like terms: 30y + 72y = 102y
(36 + 102y + 60y2) = 0

Solving
36 + 102y + 60y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '6'.
6(6 + 17y + 10y2) = 0

Factor a trinomial.
6((6 + 5y)(1 + 2y)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 2y)' equal to zero and attempt to solve:

Simplifying
1 + 2y = 0

Solving
1 + 2y = 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 + 2y = 0 + -1

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

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

Divide each side by '2'.
y = -0.5

Simplifying
y = -0.5
Solution
y = {-1.2, -0.5}