10a^2+67a+42=0

Solution for 10a^2+67a+42=0 equation:

Simplifying
10a2 + 67a + 42 = 0

Reorder the terms:
42 + 67a + 10a2 = 0

Solving
42 + 67a + 10a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6 + a)(7 + 10a) = 0

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

Simplifying
6 + a = 0

Solving
6 + a = 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 + a = 0 + -6

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

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

Simplifying
a = -6
Subproblem 2
Set the factor '(7 + 10a)' equal to zero and attempt to solve:

Simplifying
7 + 10a = 0

Solving
7 + 10a = 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 + 10a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 10a = 0 + -7
10a = 0 + -7

Combine like terms: 0 + -7 = -7
10a = -7

Divide each side by '10'.
a = -0.7

Simplifying
a = -0.7
Solution
a = {-6, -0.7}