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

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

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

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

Reorder the terms:
-10a + 2a2 = 4(-5 + a)
-10a + 2a2 = (-5 * 4 + a * 4)
-10a + 2a2 = (-20 + 4a)

Solving
-10a + 2a2 = -20 + 4a

Solving for variable 'a'.

Reorder the terms:
20 + -10a + -4a + 2a2 = -20 + 4a + 20 + -4a

Combine like terms: -10a + -4a = -14a
20 + -14a + 2a2 = -20 + 4a + 20 + -4a

Reorder the terms:
20 + -14a + 2a2 = -20 + 20 + 4a + -4a

Combine like terms: -20 + 20 = 0
20 + -14a + 2a2 = 0 + 4a + -4a
20 + -14a + 2a2 = 4a + -4a

Combine like terms: 4a + -4a = 0
20 + -14a + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -7a + 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}