5b^2-9=12b

Solution for 5b^2-9=12b equation:

Simplifying
5b2 + -9 = 12b

Reorder the terms:
-9 + 5b2 = 12b

Solving
-9 + 5b2 = 12b

Solving for variable 'b'.

Reorder the terms:
-9 + -12b + 5b2 = 12b + -12b

Combine like terms: 12b + -12b = 0
-9 + -12b + 5b2 = 0

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

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

Simplifying
-3 + -5b = 0

Solving
-3 + -5b = 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 + -5b = 0 + 3

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

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

Divide each side by '-5'.
b = -0.6

Simplifying
b = -0.6
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 = {-0.6, 3}