0=6-23a-4a^2

Solution for 0=6-23a-4a^2 equation:

Simplifying
0 = 6 + -23a + -4a2

Solving
0 = 6 + -23a + -4a2

Solving for variable 'a'.

Combine like terms: 0 + -6 = -6
-6 + 23a + 4a2 = 6 + -23a + -4a2 + -6 + 23a + 4a2

Reorder the terms:
-6 + 23a + 4a2 = 6 + -6 + -23a + 23a + -4a2 + 4a2

Combine like terms: 6 + -6 = 0
-6 + 23a + 4a2 = 0 + -23a + 23a + -4a2 + 4a2
-6 + 23a + 4a2 = -23a + 23a + -4a2 + 4a2

Combine like terms: -23a + 23a = 0
-6 + 23a + 4a2 = 0 + -4a2 + 4a2
-6 + 23a + 4a2 = -4a2 + 4a2

Combine like terms: -4a2 + 4a2 = 0
-6 + 23a + 4a2 = 0

Factor a trinomial.
(-6 + -1a)(1 + -4a) = 0

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

Simplifying
-6 + -1a = 0

Solving
-6 + -1a = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1a = 0 + 6
-1a = 0 + 6

Combine like terms: 0 + 6 = 6
-1a = 6

Divide each side by '-1'.
a = -6

Simplifying
a = -6
Subproblem 2
Set the factor '(1 + -4a)' equal to zero and attempt to solve:

Simplifying
1 + -4a = 0

Solving
1 + -4a = 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 + -4a = 0 + -1

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

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

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {-6, 0.25}