3a^2+9a-84=0

Solution for 3a^2+9a-84=0 equation:

Simplifying
3a2 + 9a + -84 = 0

Reorder the terms:
-84 + 9a + 3a2 = 0

Solving
-84 + 9a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + 3a + a2) = 0

Factor a trinomial.
3((-7 + -1a)(4 + -1a)) = 0

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

Simplifying
-7 + -1a = 0

Solving
-7 + -1a = 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 + -1a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1a = 0 + 7
-1a = 0 + 7

Combine like terms: 0 + 7 = 7
-1a = 7

Divide each side by '-1'.
a = -7

Simplifying
a = -7
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-7, 4}