2a(a-5)+4(a-5)=0

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

Simplifying
2a(a + -5) + 4(a + -5) = 0

Reorder the terms:
2a(-5 + a) + 4(a + -5) = 0
(-5 * 2a + a * 2a) + 4(a + -5) = 0
(-10a + 2a2) + 4(a + -5) = 0

Reorder the terms:
-10a + 2a2 + 4(-5 + a) = 0
-10a + 2a2 + (-5 * 4 + a * 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}