-21-8a=5a(a+6)

Solution for -21-8a=5a(a+6) equation:

Simplifying
-21 + -8a = 5a(a + 6)

Reorder the terms:
-21 + -8a = 5a(6 + a)
-21 + -8a = (6 * 5a + a * 5a)
-21 + -8a = (30a + 5a2)

Solving
-21 + -8a = 30a + 5a2

Solving for variable 'a'.

Combine like terms: -8a + -30a = -38a
-21 + -38a + -5a2 = 30a + 5a2 + -30a + -5a2

Reorder the terms:
-21 + -38a + -5a2 = 30a + -30a + 5a2 + -5a2

Combine like terms: 30a + -30a = 0
-21 + -38a + -5a2 = 0 + 5a2 + -5a2
-21 + -38a + -5a2 = 5a2 + -5a2

Combine like terms: 5a2 + -5a2 = 0
-21 + -38a + -5a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 38a + 5a2) = 0

Factor a trinomial.
-1((7 + a)(3 + 5a)) = 0

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

Simplifying
7 + a = 0

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

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

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

Simplifying
a = -7
Subproblem 2
Set the factor '(3 + 5a)' equal to zero and attempt to solve:

Simplifying
3 + 5a = 0

Solving
3 + 5a = 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 + 5a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5a = 0 + -3
5a = 0 + -3

Combine like terms: 0 + -3 = -3
5a = -3

Divide each side by '5'.
a = -0.6

Simplifying
a = -0.6
Solution
a = {-7, -0.6}