4y(6y^2+7y+6)=

Solution for 4y(6y^2+7y+6)= equation:

Simplifying
4y(6y2 + 7y + 6) = 0

Reorder the terms:
4y(6 + 7y + 6y2) = 0
(6 * 4y + 7y * 4y + 6y2 * 4y) = 0
(24y + 28y2 + 24y3) = 0

Solving
24y + 28y2 + 24y3 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '4y'.
4y(6 + 7y + 6y2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(6 + 7y + 6y2)' equal to zero and attempt to solve:

Simplifying
6 + 7y + 6y2 = 0

Solving
6 + 7y + 6y2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
1 + 1.166666667y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.166666667y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + 1.166666667y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.166666667y + y2 = 0 + -1
1.166666667y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.166666667y + y2 = -1

The y term is 1.166666667y.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667y + 0.3402777780 + y2 = -1 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667y + y2 = -1 + 0.3402777780

Combine like terms: -1 + 0.3402777780 = -0.659722222
0.3402777780 + 1.166666667y + y2 = -0.659722222

Factor a perfect square on the left side:
(y + 0.5833333335)(y + 0.5833333335) = -0.659722222

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
y = {0}