10c^2+23c-42=0

Solution for 10c^2+23c-42=0 equation:

Simplifying
10c2 + 23c + -42 = 0

Reorder the terms:
-42 + 23c + 10c2 = 0

Solving
-42 + 23c + 10c2 = 0

Solving for variable 'c'.

Factor a trinomial.
(-7 + -2c)(6 + -5c) = 0

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

Simplifying
-7 + -2c = 0

Solving
-7 + -2c = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2c = 0 + 7

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

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

Divide each side by '-2'.
c = -3.5

Simplifying
c = -3.5
Subproblem 2
Set the factor '(6 + -5c)' equal to zero and attempt to solve:

Simplifying
6 + -5c = 0

Solving
6 + -5c = 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 + -5c = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5c = 0 + -6
-5c = 0 + -6

Combine like terms: 0 + -6 = -6
-5c = -6

Divide each side by '-5'.
c = 1.2

Simplifying
c = 1.2
Solution
c = {-3.5, 1.2}