2A(1A-5)+4(1A-5)=0

Solution for 2A(1A-5)+4(1A-5)=0 equation:

Simplifying
2A(1A + -5) + 4(1A + -5) = 0

Reorder the terms:
2A(-5 + 1A) + 4(1A + -5) = 0
(-5 * 2A + 1A * 2A) + 4(1A + -5) = 0
(-10A + 2A2) + 4(1A + -5) = 0

Reorder the terms:
-10A + 2A2 + 4(-5 + 1A) = 0
-10A + 2A2 + (-5 * 4 + 1A * 4) = 0
-10A + 2A2 + (-20 + 4A) = 0

Reorder the terms:
-20 + -10A + 4A + 2A2 = 0

Combine like terms: -10A + 4A = -6A
-20 + -6A + 2A2 = 0

Solving
-20 + -6A + 2A2 = 0

Solving for variable 'A'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3A + A2) = 0

Factor a trinomial.
2((-2 + -1A)(5 + -1A)) = 0

Ignore the factor 2.
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 '(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
Solution
A = {-2, 5}