(5c+1)(8c-3)=0

Solution for (5c+1)(8c-3)=0 equation:

Simplifying
(5c + 1)(8c + -3) = 0

Reorder the terms:
(1 + 5c)(8c + -3) = 0

Reorder the terms:
(1 + 5c)(-3 + 8c) = 0

Multiply (1 + 5c) * (-3 + 8c)
(1(-3 + 8c) + 5c * (-3 + 8c)) = 0
((-3 * 1 + 8c * 1) + 5c * (-3 + 8c)) = 0
((-3 + 8c) + 5c * (-3 + 8c)) = 0
(-3 + 8c + (-3 * 5c + 8c * 5c)) = 0
(-3 + 8c + (-15c + 40c2)) = 0

Combine like terms: 8c + -15c = -7c
(-3 + -7c + 40c2) = 0

Solving
-3 + -7c + 40c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-1 + -5c)(3 + -8c) = 0

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

Simplifying
-1 + -5c = 0

Solving
-1 + -5c = 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 + -5c = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5c = 0 + 1
-5c = 0 + 1

Combine like terms: 0 + 1 = 1
-5c = 1

Divide each side by '-5'.
c = -0.2

Simplifying
c = -0.2
Subproblem 2
Set the factor '(3 + -8c)' equal to zero and attempt to solve:

Simplifying
3 + -8c = 0

Solving
3 + -8c = 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 + -8c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8c = 0 + -3
-8c = 0 + -3

Combine like terms: 0 + -3 = -3
-8c = -3

Divide each side by '-8'.
c = 0.375

Simplifying
c = 0.375
Solution
c = {-0.2, 0.375}