4b^2+9=12b

Solution for 4b^2+9=12b equation:

Simplifying
4b2 + 9 = 12b

Reorder the terms:
9 + 4b2 = 12b

Solving
9 + 4b2 = 12b

Solving for variable 'b'.

Reorder the terms:
9 + -12b + 4b2 = 12b + -12b

Combine like terms: 12b + -12b = 0
9 + -12b + 4b2 = 0

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

Subproblem 1
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
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 = {1.5, 1.5}