(2c+1)(3c-2)=55

Solution for (2c+1)(3c-2)=55 equation:

Simplifying
(2c + 1)(3c + -2) = 55

Reorder the terms:
(1 + 2c)(3c + -2) = 55

Reorder the terms:
(1 + 2c)(-2 + 3c) = 55

Multiply (1 + 2c) * (-2 + 3c)
(1(-2 + 3c) + 2c * (-2 + 3c)) = 55
((-2 * 1 + 3c * 1) + 2c * (-2 + 3c)) = 55
((-2 + 3c) + 2c * (-2 + 3c)) = 55
(-2 + 3c + (-2 * 2c + 3c * 2c)) = 55
(-2 + 3c + (-4c + 6c2)) = 55

Combine like terms: 3c + -4c = -1c
(-2 + -1c + 6c2) = 55

Solving
-2 + -1c + 6c2 = 55

Solving for variable 'c'.

Reorder the terms:
-2 + -55 + -1c + 6c2 = 55 + -55

Combine like terms: -2 + -55 = -57
-57 + -1c + 6c2 = 55 + -55

Combine like terms: 55 + -55 = 0
-57 + -1c + 6c2 = 0

Factor a trinomial.
(-3 + -1c)(19 + -6c) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(19 + -6c)' equal to zero and attempt to solve:

Simplifying
19 + -6c = 0

Solving
19 + -6c = 0

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

Add '-19' to each side of the equation.
19 + -19 + -6c = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -6c = 0 + -19
-6c = 0 + -19

Combine like terms: 0 + -19 = -19
-6c = -19

Divide each side by '-6'.
c = 3.166666667

Simplifying
c = 3.166666667
Solution
c = {-3, 3.166666667}