6a^2+16a-22=0

Solution for 6a^2+16a-22=0 equation:

Simplifying
6a2 + 16a + -22 = 0

Reorder the terms:
-22 + 16a + 6a2 = 0

Solving
-22 + 16a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 8a + 3a2) = 0

Factor a trinomial.
2((-11 + -3a)(1 + -1a)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-11 + -3a)' equal to zero and attempt to solve:

Simplifying
-11 + -3a = 0

Solving
-11 + -3a = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3a = 0 + 11
-3a = 0 + 11

Combine like terms: 0 + 11 = 11
-3a = 11

Divide each side by '-3'.
a = -3.666666667

Simplifying
a = -3.666666667
Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Solution
a = {-3.666666667, 1}