3a^2-2a-21=0

Solution for 3a^2-2a-21=0 equation:

Simplifying
3a2 + -2a + -21 = 0

Reorder the terms:
-21 + -2a + 3a2 = 0

Solving
-21 + -2a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -3a)(3 + -1a) = 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 '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 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 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-2.333333333, 3}