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

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

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

Reorder the terms:
(-2 + a)(a + 1) = -2a

Reorder the terms:
(-2 + a)(1 + a) = -2a

Multiply (-2 + a) * (1 + a)
(-2(1 + a) + a(1 + a)) = -2a
((1 * -2 + a * -2) + a(1 + a)) = -2a
((-2 + -2a) + a(1 + a)) = -2a
(-2 + -2a + (1 * a + a * a)) = -2a
(-2 + -2a + (1a + a2)) = -2a

Combine like terms: -2a + 1a = -1a
(-2 + -1a + a2) = -2a

Solving
-2 + -1a + a2 = -2a

Solving for variable 'a'.

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

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

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

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

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

Simplifying
-2 + -1a = 0

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

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

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

Divide each side by '-1'.
a = -2

Simplifying
a = -2
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 = {-2, 1}