4b(3b-6)=-9

Solution for 4b(3b-6)=-9 equation:

Simplifying
4b(3b + -6) = -9

Reorder the terms:
4b(-6 + 3b) = -9
(-6 * 4b + 3b * 4b) = -9
(-24b + 12b2) = -9

Solving
-24b + 12b2 = -9

Solving for variable 'b'.

Reorder the terms:
9 + -24b + 12b2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -24b + 12b2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -8b + 4b2) = 0

Factor a trinomial.
3((1 + -2b)(3 + -2b)) = 0

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

Simplifying
1 + -2b = 0

Solving
1 + -2b = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2b = 0 + -1

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

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

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

Simplifying
b = 0.5
Subproblem 2
Set the factor '(3 + -2b)' equal to zero and attempt to solve:

Simplifying
3 + -2b = 0

Solving
3 + -2b = 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 + -2b = 0 + -3

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

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

Divide each side by '-2'.
b = 1.5

Simplifying
b = 1.5
Solution
b = {0.5, 1.5}