4c(c-2)=6-3c

Solution for 4c(c-2)=6-3c equation:

Simplifying
4c(c + -2) = 6 + -3c

Reorder the terms:
4c(-2 + c) = 6 + -3c
(-2 * 4c + c * 4c) = 6 + -3c
(-8c + 4c2) = 6 + -3c

Solving
-8c + 4c2 = 6 + -3c

Solving for variable 'c'.

Reorder the terms:
-6 + -8c + 3c + 4c2 = 6 + -3c + -6 + 3c

Combine like terms: -8c + 3c = -5c
-6 + -5c + 4c2 = 6 + -3c + -6 + 3c

Reorder the terms:
-6 + -5c + 4c2 = 6 + -6 + -3c + 3c

Combine like terms: 6 + -6 = 0
-6 + -5c + 4c2 = 0 + -3c + 3c
-6 + -5c + 4c2 = -3c + 3c

Combine like terms: -3c + 3c = 0
-6 + -5c + 4c2 = 0

Factor a trinomial.
(-3 + -4c)(2 + -1c) = 0

Subproblem 1
Set the factor '(-3 + -4c)' equal to zero and attempt to solve:

Simplifying
-3 + -4c = 0

Solving
-3 + -4c = 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 + -4c = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4c = 0 + 3
-4c = 0 + 3

Combine like terms: 0 + 3 = 3
-4c = 3

Divide each side by '-4'.
c = -0.75

Simplifying
c = -0.75
Subproblem 2
Set the factor '(2 + -1c)' equal to zero and attempt to solve:

Simplifying
2 + -1c = 0

Solving
2 + -1c = 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 + -1c = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1c = 0 + -2
-1c = 0 + -2

Combine like terms: 0 + -2 = -2
-1c = -2

Divide each side by '-1'.
c = 2

Simplifying
c = 2
Solution
c = {-0.75, 2}