0=3c^2-45c+42

Solution for 0=3c^2-45c+42 equation:

Simplifying
0 = 3c2 + -45c + 42

Reorder the terms:
0 = 42 + -45c + 3c2

Solving
0 = 42 + -45c + 3c2

Solving for variable 'c'.

Combine like terms: 0 + -42 = -42
-42 + 45c + -3c2 = 42 + -45c + 3c2 + -42 + 45c + -3c2

Reorder the terms:
-42 + 45c + -3c2 = 42 + -42 + -45c + 45c + 3c2 + -3c2

Combine like terms: 42 + -42 = 0
-42 + 45c + -3c2 = 0 + -45c + 45c + 3c2 + -3c2
-42 + 45c + -3c2 = -45c + 45c + 3c2 + -3c2

Combine like terms: -45c + 45c = 0
-42 + 45c + -3c2 = 0 + 3c2 + -3c2
-42 + 45c + -3c2 = 3c2 + -3c2

Combine like terms: 3c2 + -3c2 = 0
-42 + 45c + -3c2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 15c + -1c2) = 0

Factor a trinomial.
3((-14 + c)(1 + -1c)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-14 + c)' equal to zero and attempt to solve:

Simplifying
-14 + c = 0

Solving
-14 + c = 0

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

Add '14' to each side of the equation.
-14 + 14 + c = 0 + 14

Combine like terms: -14 + 14 = 0
0 + c = 0 + 14
c = 0 + 14

Combine like terms: 0 + 14 = 14
c = 14

Simplifying
c = 14
Subproblem 2
Set the factor '(1 + -1c)' equal to zero and attempt to solve:

Simplifying
1 + -1c = 0

Solving
1 + -1c = 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 + -1c = 0 + -1

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

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

Divide each side by '-1'.
c = 1

Simplifying
c = 1
Solution
c = {14, 1}