3a^2+13a-126=0

Solution for 3a^2+13a-126=0 equation:

Simplifying
3a2 + 13a + -126 = 0

Reorder the terms:
-126 + 13a + 3a2 = 0

Solving
-126 + 13a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -1a)(14 + -3a) = 0

Subproblem 1
Set the factor '(-9 + -1a)' equal to zero and attempt to solve:

Simplifying
-9 + -1a = 0

Solving
-9 + -1a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1a = 0 + 9
-1a = 0 + 9

Combine like terms: 0 + 9 = 9
-1a = 9

Divide each side by '-1'.
a = -9

Simplifying
a = -9
Subproblem 2
Set the factor '(14 + -3a)' equal to zero and attempt to solve:

Simplifying
14 + -3a = 0

Solving
14 + -3a = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3a = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3a = 0 + -14
-3a = 0 + -14

Combine like terms: 0 + -14 = -14
-3a = -14

Divide each side by '-3'.
a = 4.666666667

Simplifying
a = 4.666666667
Solution
a = {-9, 4.666666667}