4a^2-31a+42=0

Solution for 4a^2-31a+42=0 equation:

Simplifying
4a2 + -31a + 42 = 0

Reorder the terms:
42 + -31a + 4a2 = 0

Solving
42 + -31a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(7 + -4a)(6 + -1a) = 0

Subproblem 1
Set the factor '(7 + -4a)' equal to zero and attempt to solve:

Simplifying
7 + -4a = 0

Solving
7 + -4a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -4a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4a = 0 + -7
-4a = 0 + -7

Combine like terms: 0 + -7 = -7
-4a = -7

Divide each side by '-4'.
a = 1.75

Simplifying
a = 1.75
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {1.75, 6}