y(-3+7b)(6-9b)=

Solution for y(-3+7b)(6-9b)= equation:

Simplifying
y(-3 + 7b)(6 + -9b) = 0

Multiply (-3 + 7b) * (6 + -9b)
y(-3(6 + -9b) + 7b * (6 + -9b)) = 0
y((6 * -3 + -9b * -3) + 7b * (6 + -9b)) = 0
y((-18 + 27b) + 7b * (6 + -9b)) = 0
y(-18 + 27b + (6 * 7b + -9b * 7b)) = 0
y(-18 + 27b + (42b + -63b2)) = 0

Combine like terms: 27b + 42b = 69b
y(-18 + 69b + -63b2) = 0
(-18 * y + 69b * y + -63b2 * y) = 0

Reorder the terms:
(69by + -63b2y + -18y) = 0
(69by + -63b2y + -18y) = 0

Solving
69by + -63b2y + -18y = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3y'.
3y(23b + -21b2 + -6) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor 'y' equal to zero and attempt to solve:

Simplifying
y = 0

Solving
y = 0

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

Add '-1y' to each side of the equation.
y + -1y = 0 + -1y
Remove the zero:
0 = -1y

Simplifying
0 = -1y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-7b + 3)' equal to zero and attempt to solve:

Simplifying
-7b + 3 = 0

Reorder the terms:
3 + -7b = 0

Solving
3 + -7b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7b = 0 + -3
-7b = 0 + -3

Combine like terms: 0 + -3 = -3
-7b = -3

Divide each side by '-7'.
b = 0.4285714286

Simplifying
b = 0.4285714286
Subproblem 3
Set the factor '(3b + -2)' equal to zero and attempt to solve:

Simplifying
3b + -2 = 0

Reorder the terms:
-2 + 3b = 0

Solving
-2 + 3b = 0

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

Add '2' to each side of the equation.
-2 + 2 + 3b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3b = 0 + 2
3b = 0 + 2

Combine like terms: 0 + 2 = 2
3b = 2

Divide each side by '3'.
b = 0.6666666667

Simplifying
b = 0.6666666667
Solution
b = {0.4285714286, 0.6666666667}