(2c-15)(6c+36)=0

Solution for (2c-15)(6c+36)=0 equation:

Simplifying
(2c + -15)(6c + 36) = 0

Reorder the terms:
(-15 + 2c)(6c + 36) = 0

Reorder the terms:
(-15 + 2c)(36 + 6c) = 0

Multiply (-15 + 2c) * (36 + 6c)
(-15(36 + 6c) + 2c * (36 + 6c)) = 0
((36 * -15 + 6c * -15) + 2c * (36 + 6c)) = 0
((-540 + -90c) + 2c * (36 + 6c)) = 0
(-540 + -90c + (36 * 2c + 6c * 2c)) = 0
(-540 + -90c + (72c + 12c2)) = 0

Combine like terms: -90c + 72c = -18c
(-540 + -18c + 12c2) = 0

Solving
-540 + -18c + 12c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-90 + -3c + 2c2) = 0

Factor a trinomial.
6((-6 + -1c)(15 + -2c)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(15 + -2c)' equal to zero and attempt to solve:

Simplifying
15 + -2c = 0

Solving
15 + -2c = 0

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

Add '-15' to each side of the equation.
15 + -15 + -2c = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -2c = 0 + -15
-2c = 0 + -15

Combine like terms: 0 + -15 = -15
-2c = -15

Divide each side by '-2'.
c = 7.5

Simplifying
c = 7.5
Solution
c = {-6, 7.5}