7c^2-35c+42=0

Solution for 7c^2-35c+42=0 equation:

Simplifying
7c2 + -35c + 42 = 0

Reorder the terms:
42 + -35c + 7c2 = 0

Solving
42 + -35c + 7c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '7'.
7(6 + -5c + c2) = 0

Factor a trinomial.
7((2 + -1c)(3 + -1c)) = 0

Ignore the factor 7.
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 + -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
Solution
c = {2, 3}