6a^2+11a-21=0

Solution for 6a^2+11a-21=0 equation:

Simplifying
6a2 + 11a + -21 = 0

Reorder the terms:
-21 + 11a + 6a2 = 0

Solving
-21 + 11a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(7 + -6a) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -6a)' equal to zero and attempt to solve:

Simplifying
7 + -6a = 0

Solving
7 + -6a = 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 + -6a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6a = 0 + -7
-6a = 0 + -7

Combine like terms: 0 + -7 = -7
-6a = -7

Divide each side by '-6'.
a = 1.166666667

Simplifying
a = 1.166666667
Solution
a = {-3, 1.166666667}