12a^2-10a-42=

Solution for 12a^2-10a-42= equation:

Simplifying
12a2 + -10a + -42 = 0

Reorder the terms:
-42 + -10a + 12a2 = 0

Solving
-42 + -10a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -5a + 6a2) = 0

Factor a trinomial.
2((-3 + -2a)(7 + -3a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve:

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
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
Solution
a = {-1.5, 2.333333333}