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

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

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

Reorder the terms:
5c(-2 + c) = 6 + 3c
(-2 * 5c + c * 5c) = 6 + 3c
(-10c + 5c2) = 6 + 3c

Solving
-10c + 5c2 = 6 + 3c

Solving for variable 'c'.

Reorder the terms:
-6 + -10c + -3c + 5c2 = 6 + 3c + -6 + -3c

Combine like terms: -10c + -3c = -13c
-6 + -13c + 5c2 = 6 + 3c + -6 + -3c

Reorder the terms:
-6 + -13c + 5c2 = 6 + -6 + 3c + -3c

Combine like terms: 6 + -6 = 0
-6 + -13c + 5c2 = 0 + 3c + -3c
-6 + -13c + 5c2 = 3c + -3c

Combine like terms: 3c + -3c = 0
-6 + -13c + 5c2 = 0

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

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

Simplifying
-2 + -5c = 0

Solving
-2 + -5c = 0

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

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

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

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

Divide each side by '-5'.
c = -0.4

Simplifying
c = -0.4
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 = {-0.4, 3}