15a^2+17a-42=0

Solution for 15a^2+17a-42=0 equation:

Simplifying
15a2 + 17a + -42 = 0

Reorder the terms:
-42 + 17a + 15a2 = 0

Solving
-42 + 17a + 15a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -3a)(6 + -5a) = 0

Subproblem 1
Set the factor '(-7 + -3a)' equal to zero and attempt to solve:

Simplifying
-7 + -3a = 0

Solving
-7 + -3a = 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 + -3a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3a = 0 + 7
-3a = 0 + 7

Combine like terms: 0 + 7 = 7
-3a = 7

Divide each side by '-3'.
a = -2.333333333

Simplifying
a = -2.333333333
Subproblem 2
Set the factor '(6 + -5a)' equal to zero and attempt to solve:

Simplifying
6 + -5a = 0

Solving
6 + -5a = 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 + -5a = 0 + -6

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

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

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

Simplifying
a = 1.2
Solution
a = {-2.333333333, 1.2}