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

Solution for (4c+3)(c-6)=0 equation:

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

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

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

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

Combine like terms: 3c + -24c = -21c
(-18 + -21c + 4c2) = 0

Solving
-18 + -21c + 4c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-3 + -4c)(6 + -1c) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1c)' equal to zero and attempt to solve:

Simplifying
6 + -1c = 0

Solving
6 + -1c = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1c = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1c = 0 + -6
-1c = 0 + -6

Combine like terms: 0 + -6 = -6
-1c = -6

Divide each side by '-1'.
c = 6

Simplifying
c = 6
Solution
c = {-0.75, 6}