2(9b^2+12b-5)=0

Solution for 2(9b^2+12b-5)=0 equation:

Simplifying
2(9b2 + 12b + -5) = 0

Reorder the terms:
2(-5 + 12b + 9b2) = 0
(-5 * 2 + 12b * 2 + 9b2 * 2) = 0
(-10 + 24b + 18b2) = 0

Solving
-10 + 24b + 18b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 12b + 9b2) = 0

Factor a trinomial.
2((-5 + -3b)(1 + -3b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -3b)' equal to zero and attempt to solve:

Simplifying
-5 + -3b = 0

Solving
-5 + -3b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3b = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3b = 0 + 5
-3b = 0 + 5

Combine like terms: 0 + 5 = 5
-3b = 5

Divide each side by '-3'.
b = -1.666666667

Simplifying
b = -1.666666667
Subproblem 2
Set the factor '(1 + -3b)' equal to zero and attempt to solve:

Simplifying
1 + -3b = 0

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

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

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

Divide each side by '-3'.
b = 0.3333333333

Simplifying
b = 0.3333333333
Solution
b = {-1.666666667, 0.3333333333}