8-2a(a+1)=9+a

Solution for 8-2a(a+1)=9+a equation:

Simplifying
8 + -2a(a + 1) = 9 + a

Reorder the terms:
8 + -2a(1 + a) = 9 + a
8 + (1 * -2a + a * -2a) = 9 + a
8 + (-2a + -2a2) = 9 + a

Solving
8 + -2a + -2a2 = 9 + a

Solving for variable 'a'.

Reorder the terms:
8 + -9 + -2a + -1a + -2a2 = 9 + a + -9 + -1a

Combine like terms: 8 + -9 = -1
-1 + -2a + -1a + -2a2 = 9 + a + -9 + -1a

Combine like terms: -2a + -1a = -3a
-1 + -3a + -2a2 = 9 + a + -9 + -1a

Reorder the terms:
-1 + -3a + -2a2 = 9 + -9 + a + -1a

Combine like terms: 9 + -9 = 0
-1 + -3a + -2a2 = 0 + a + -1a
-1 + -3a + -2a2 = a + -1a

Combine like terms: a + -1a = 0
-1 + -3a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 3a + 2a2) = 0

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

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

Simplifying
1 + a = 0

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

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

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

Simplifying
a = -1
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 = {-1, -0.5}