(5c+3)(2c-6)=0

Solution for (5c+3)(2c-6)=0 equation:

Simplifying
(5c + 3)(2c + -6) = 0

Reorder the terms:
(3 + 5c)(2c + -6) = 0

Reorder the terms:
(3 + 5c)(-6 + 2c) = 0

Multiply (3 + 5c) * (-6 + 2c)
(3(-6 + 2c) + 5c * (-6 + 2c)) = 0
((-6 * 3 + 2c * 3) + 5c * (-6 + 2c)) = 0
((-18 + 6c) + 5c * (-6 + 2c)) = 0
(-18 + 6c + (-6 * 5c + 2c * 5c)) = 0
(-18 + 6c + (-30c + 10c2)) = 0

Combine like terms: 6c + -30c = -24c
(-18 + -24c + 10c2) = 0

Solving
-18 + -24c + 10c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -12c + 5c2) = 0

Factor a trinomial.
2((-3 + -5c)(3 + -1c)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -5c)' equal to zero and attempt to solve:

Simplifying
-3 + -5c = 0

Solving
-3 + -5c = 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 + -5c = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5c = 0 + 3
-5c = 0 + 3

Combine like terms: 0 + 3 = 3
-5c = 3

Divide each side by '-5'.
c = -0.6

Simplifying
c = -0.6
Subproblem 2
Set the factor '(3 + -1c)' equal to zero and attempt to solve:

Simplifying
3 + -1c = 0

Solving
3 + -1c = 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 + -1c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1c = 0 + -3
-1c = 0 + -3

Combine like terms: 0 + -3 = -3
-1c = -3

Divide each side by '-1'.
c = 3

Simplifying
c = 3
Solution
c = {-0.6, 3}