(-7c+2)(2c+3)=0

Solution for (-7c+2)(2c+3)=0 equation:

Simplifying
(-7c + 2)(2c + 3) = 0

Reorder the terms:
(2 + -7c)(2c + 3) = 0

Reorder the terms:
(2 + -7c)(3 + 2c) = 0

Multiply (2 + -7c) * (3 + 2c)
(2(3 + 2c) + -7c * (3 + 2c)) = 0
((3 * 2 + 2c * 2) + -7c * (3 + 2c)) = 0
((6 + 4c) + -7c * (3 + 2c)) = 0
(6 + 4c + (3 * -7c + 2c * -7c)) = 0
(6 + 4c + (-21c + -14c2)) = 0

Combine like terms: 4c + -21c = -17c
(6 + -17c + -14c2) = 0

Solving
6 + -17c + -14c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(2 + -7c)(3 + 2c) = 0

Subproblem 1
Set the factor '(2 + -7c)' equal to zero and attempt to solve:

Simplifying
2 + -7c = 0

Solving
2 + -7c = 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 + -7c = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7c = 0 + -2
-7c = 0 + -2

Combine like terms: 0 + -2 = -2
-7c = -2

Divide each side by '-7'.
c = 0.2857142857

Simplifying
c = 0.2857142857
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 = {0.2857142857, -1.5}