8c(2c-3)-9(2c-3)=0

Solution for 8c(2c-3)-9(2c-3)=0 equation:

Simplifying
8c(2c + -3) + -9(2c + -3) = 0

Reorder the terms:
8c(-3 + 2c) + -9(2c + -3) = 0
(-3 * 8c + 2c * 8c) + -9(2c + -3) = 0
(-24c + 16c2) + -9(2c + -3) = 0

Reorder the terms:
-24c + 16c2 + -9(-3 + 2c) = 0
-24c + 16c2 + (-3 * -9 + 2c * -9) = 0
-24c + 16c2 + (27 + -18c) = 0

Reorder the terms:
27 + -24c + -18c + 16c2 = 0

Combine like terms: -24c + -18c = -42c
27 + -42c + 16c2 = 0

Solving
27 + -42c + 16c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(9 + -8c)(3 + -2c) = 0

Subproblem 1
Set the factor '(9 + -8c)' equal to zero and attempt to solve:

Simplifying
9 + -8c = 0

Solving
9 + -8c = 0

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

Add '-9' to each side of the equation.
9 + -9 + -8c = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8c = 0 + -9
-8c = 0 + -9

Combine like terms: 0 + -9 = -9
-8c = -9

Divide each side by '-8'.
c = 1.125

Simplifying
c = 1.125
Subproblem 2
Set the factor '(3 + -2c)' equal to zero and attempt to solve:

Simplifying
3 + -2c = 0

Solving
3 + -2c = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2c = 0 + -3

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

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

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

Simplifying
c = 1.5
Solution
c = {1.125, 1.5}