6-2a(a+2)=8+a

Solution for 6-2a(a+2)=8+a equation:

Simplifying
6 + -2a(a + 2) = 8 + a

Reorder the terms:
6 + -2a(2 + a) = 8 + a
6 + (2 * -2a + a * -2a) = 8 + a
6 + (-4a + -2a2) = 8 + a

Solving
6 + -4a + -2a2 = 8 + a

Solving for variable 'a'.

Reorder the terms:
6 + -8 + -4a + -1a + -2a2 = 8 + a + -8 + -1a

Combine like terms: 6 + -8 = -2
-2 + -4a + -1a + -2a2 = 8 + a + -8 + -1a

Combine like terms: -4a + -1a = -5a
-2 + -5a + -2a2 = 8 + a + -8 + -1a

Reorder the terms:
-2 + -5a + -2a2 = 8 + -8 + a + -1a

Combine like terms: 8 + -8 = 0
-2 + -5a + -2a2 = 0 + a + -1a
-2 + -5a + -2a2 = a + -1a

Combine like terms: a + -1a = 0
-2 + -5a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 5a + 2a2) = 0

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

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

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

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

Simplifying
1 + 2a = 0

Solving
1 + 2a = 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 + 2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2a = 0 + -1
2a = 0 + -1

Combine like terms: 0 + -1 = -1
2a = -1

Divide each side by '2'.
a = -0.5

Simplifying
a = -0.5
Solution
a = {-2, -0.5}