(4c-3)(6c+9)=

Solution for (4c-3)(6c+9)= equation:

Simplifying
(4c + -3)(6c + 9) = 0

Reorder the terms:
(-3 + 4c)(6c + 9) = 0

Reorder the terms:
(-3 + 4c)(9 + 6c) = 0

Multiply (-3 + 4c) * (9 + 6c)
(-3(9 + 6c) + 4c * (9 + 6c)) = 0
((9 * -3 + 6c * -3) + 4c * (9 + 6c)) = 0
((-27 + -18c) + 4c * (9 + 6c)) = 0
(-27 + -18c + (9 * 4c + 6c * 4c)) = 0
(-27 + -18c + (36c + 24c2)) = 0

Combine like terms: -18c + 36c = 18c
(-27 + 18c + 24c2) = 0

Solving
-27 + 18c + 24c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + 6c + 8c2) = 0

Factor a trinomial.
3((-3 + -2c)(3 + -4c)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -4c)' equal to zero and attempt to solve:

Simplifying
3 + -4c = 0

Solving
3 + -4c = 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 + -4c = 0 + -3

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

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

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

Simplifying
c = 0.75
Solution
c = {-1.5, 0.75}