(a-5)(a+4)=-2a

Solution for (a-5)(a+4)=-2a equation:

Simplifying
(a + -5)(a + 4) = -2a

Reorder the terms:
(-5 + a)(a + 4) = -2a

Reorder the terms:
(-5 + a)(4 + a) = -2a

Multiply (-5 + a) * (4 + a)
(-5(4 + a) + a(4 + a)) = -2a
((4 * -5 + a * -5) + a(4 + a)) = -2a
((-20 + -5a) + a(4 + a)) = -2a
(-20 + -5a + (4 * a + a * a)) = -2a
(-20 + -5a + (4a + a2)) = -2a

Combine like terms: -5a + 4a = -1a
(-20 + -1a + a2) = -2a

Solving
-20 + -1a + a2 = -2a

Solving for variable 'a'.

Reorder the terms:
-20 + -1a + 2a + a2 = -2a + 2a

Combine like terms: -1a + 2a = 1a
-20 + 1a + a2 = -2a + 2a

Combine like terms: -2a + 2a = 0
-20 + 1a + a2 = 0

Factor a trinomial.
(-5 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-5 + -1a)' equal to zero and attempt to solve:

Simplifying
-5 + -1a = 0

Solving
-5 + -1a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1a = 0 + 5

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

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

Divide each side by '-1'.
a = -5

Simplifying
a = -5
Subproblem 2
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

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

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

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Solution
a = {-5, 4}