(2c-5)(3c+1)=0

Solution for (2c-5)(3c+1)=0 equation:

Simplifying
(2c + -5)(3c + 1) = 0

Reorder the terms:
(-5 + 2c)(3c + 1) = 0

Reorder the terms:
(-5 + 2c)(1 + 3c) = 0

Multiply (-5 + 2c) * (1 + 3c)
(-5(1 + 3c) + 2c * (1 + 3c)) = 0
((1 * -5 + 3c * -5) + 2c * (1 + 3c)) = 0
((-5 + -15c) + 2c * (1 + 3c)) = 0
(-5 + -15c + (1 * 2c + 3c * 2c)) = 0
(-5 + -15c + (2c + 6c2)) = 0

Combine like terms: -15c + 2c = -13c
(-5 + -13c + 6c2) = 0

Solving
-5 + -13c + 6c2 = 0

Solving for variable 'c'.

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

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

Simplifying
-1 + -3c = 0

Solving
-1 + -3c = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3c = 0 + 1

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

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

Divide each side by '-3'.
c = -0.3333333333

Simplifying
c = -0.3333333333
Subproblem 2
Set the factor '(5 + -2c)' equal to zero and attempt to solve:

Simplifying
5 + -2c = 0

Solving
5 + -2c = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2c = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2c = 0 + -5
-2c = 0 + -5

Combine like terms: 0 + -5 = -5
-2c = -5

Divide each side by '-2'.
c = 2.5

Simplifying
c = 2.5
Solution
c = {-0.3333333333, 2.5}