16b^2-24b=-9

Solution for 16b^2-24b=-9 equation:

Simplifying
16b2 + -24b = -9

Reorder the terms:
-24b + 16b2 = -9

Solving
-24b + 16b2 = -9

Solving for variable 'b'.

Reorder the terms:
9 + -24b + 16b2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + -24b + 16b2 = 0

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

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

Simplifying
3 + -4b = 0

Solving
3 + -4b = 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 + -4b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4b = 0 + -3
-4b = 0 + -3

Combine like terms: 0 + -3 = -3
-4b = -3

Divide each side by '-4'.
b = 0.75

Simplifying
b = 0.75
Subproblem 2
Set the factor '(3 + -4b)' equal to zero and attempt to solve:

Simplifying
3 + -4b = 0

Solving
3 + -4b = 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 + -4b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4b = 0 + -3
-4b = 0 + -3

Combine like terms: 0 + -3 = -3
-4b = -3

Divide each side by '-4'.
b = 0.75

Simplifying
b = 0.75
Solution
b = {0.75, 0.75}