(7b+4)(3b-9)=0

Solution for (7b+4)(3b-9)=0 equation:

Simplifying
(7b + 4)(3b + -9) = 0

Reorder the terms:
(4 + 7b)(3b + -9) = 0

Reorder the terms:
(4 + 7b)(-9 + 3b) = 0

Multiply (4 + 7b) * (-9 + 3b)
(4(-9 + 3b) + 7b * (-9 + 3b)) = 0
((-9 * 4 + 3b * 4) + 7b * (-9 + 3b)) = 0
((-36 + 12b) + 7b * (-9 + 3b)) = 0
(-36 + 12b + (-9 * 7b + 3b * 7b)) = 0
(-36 + 12b + (-63b + 21b2)) = 0

Combine like terms: 12b + -63b = -51b
(-36 + -51b + 21b2) = 0

Solving
-36 + -51b + 21b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -17b + 7b2) = 0

Factor a trinomial.
3((-4 + -7b)(3 + -1b)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-4 + -7b)' equal to zero and attempt to solve:

Simplifying
-4 + -7b = 0

Solving
-4 + -7b = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7b = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7b = 0 + 4
-7b = 0 + 4

Combine like terms: 0 + 4 = 4
-7b = 4

Divide each side by '-7'.
b = -0.5714285714

Simplifying
b = -0.5714285714
Subproblem 2
Set the factor '(3 + -1b)' equal to zero and attempt to solve:

Simplifying
3 + -1b = 0

Solving
3 + -1b = 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 + -1b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1b = 0 + -3
-1b = 0 + -3

Combine like terms: 0 + -3 = -3
-1b = -3

Divide each side by '-1'.
b = 3

Simplifying
b = 3
Solution
b = {-0.5714285714, 3}