2c^2+3c=2c+6

Solution for 2c^2+3c=2c+6 equation:

Simplifying
2c2 + 3c = 2c + 6

Reorder the terms:
3c + 2c2 = 2c + 6

Reorder the terms:
3c + 2c2 = 6 + 2c

Solving
3c + 2c2 = 6 + 2c

Solving for variable 'c'.

Reorder the terms:
-6 + 3c + -2c + 2c2 = 6 + 2c + -6 + -2c

Combine like terms: 3c + -2c = 1c
-6 + 1c + 2c2 = 6 + 2c + -6 + -2c

Reorder the terms:
-6 + 1c + 2c2 = 6 + -6 + 2c + -2c

Combine like terms: 6 + -6 = 0
-6 + 1c + 2c2 = 0 + 2c + -2c
-6 + 1c + 2c2 = 2c + -2c

Combine like terms: 2c + -2c = 0
-6 + 1c + 2c2 = 0

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

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

Simplifying
3 + -2c = 0

Solving
3 + -2c = 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 + -2c = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2c = 0 + -3
-2c = 0 + -3

Combine like terms: 0 + -3 = -3
-2c = -3

Divide each side by '-2'.
c = 1.5

Simplifying
c = 1.5
Solution
c = {-2, 1.5}