=(3c+1)(7c-6)

Solution for =(3c+1)(7c-6) equation:

Simplifying
0 = (3c + 1)(7c + -6)

Reorder the terms:
0 = (1 + 3c)(7c + -6)

Reorder the terms:
0 = (1 + 3c)(-6 + 7c)

Multiply (1 + 3c) * (-6 + 7c)
0 = (1(-6 + 7c) + 3c * (-6 + 7c))
0 = ((-6 * 1 + 7c * 1) + 3c * (-6 + 7c))
0 = ((-6 + 7c) + 3c * (-6 + 7c))
0 = (-6 + 7c + (-6 * 3c + 7c * 3c))
0 = (-6 + 7c + (-18c + 21c2))

Combine like terms: 7c + -18c = -11c
0 = (-6 + -11c + 21c2)

Solving
0 = -6 + -11c + 21c2

Solving for variable 'c'.

Combine like terms: 0 + 6 = 6
6 + 11c + -21c2 = -6 + -11c + 21c2 + 6 + 11c + -21c2

Reorder the terms:
6 + 11c + -21c2 = -6 + 6 + -11c + 11c + 21c2 + -21c2

Combine like terms: -6 + 6 = 0
6 + 11c + -21c2 = 0 + -11c + 11c + 21c2 + -21c2
6 + 11c + -21c2 = -11c + 11c + 21c2 + -21c2

Combine like terms: -11c + 11c = 0
6 + 11c + -21c2 = 0 + 21c2 + -21c2
6 + 11c + -21c2 = 21c2 + -21c2

Combine like terms: 21c2 + -21c2 = 0
6 + 11c + -21c2 = 0

Factor a trinomial.
(6 + -7c)(1 + 3c) = 0

Subproblem 1
Set the factor '(6 + -7c)' equal to zero and attempt to solve:

Simplifying
6 + -7c = 0

Solving
6 + -7c = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7c = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7c = 0 + -6
-7c = 0 + -6

Combine like terms: 0 + -6 = -6
-7c = -6

Divide each side by '-7'.
c = 0.8571428571

Simplifying
c = 0.8571428571
Subproblem 2
Set the factor '(1 + 3c)' equal to zero and attempt to solve:

Simplifying
1 + 3c = 0

Solving
1 + 3c = 0

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

Add '-1' to each side of the equation.
1 + -1 + 3c = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3c = 0 + -1
3c = 0 + -1

Combine like terms: 0 + -1 = -1
3c = -1

Divide each side by '3'.
c = -0.3333333333

Simplifying
c = -0.3333333333
Solution
c = {0.8571428571, -0.3333333333}