2(a-5)=4a(2a-10)

Solution for 2(a-5)=4a(2a-10) equation:

Simplifying
2(a + -5) = 4a(2a + -10)

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

Reorder the terms:
-10 + 2a = 4a(-10 + 2a)
-10 + 2a = (-10 * 4a + 2a * 4a)
-10 + 2a = (-40a + 8a2)

Solving
-10 + 2a = -40a + 8a2

Solving for variable 'a'.

Combine like terms: 2a + 40a = 42a
-10 + 42a + -8a2 = -40a + 8a2 + 40a + -8a2

Reorder the terms:
-10 + 42a + -8a2 = -40a + 40a + 8a2 + -8a2

Combine like terms: -40a + 40a = 0
-10 + 42a + -8a2 = 0 + 8a2 + -8a2
-10 + 42a + -8a2 = 8a2 + -8a2

Combine like terms: 8a2 + -8a2 = 0
-10 + 42a + -8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 21a + -4a2) = 0

Factor a trinomial.
2((-5 + a)(1 + -4a)) = 0

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

Simplifying
-5 + a = 0

Solving
-5 + a = 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 + a = 0 + 5

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

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

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

Simplifying
1 + -4a = 0

Solving
1 + -4a = 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 + -4a = 0 + -1

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

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

Divide each side by '-4'.
a = 0.25

Simplifying
a = 0.25
Solution
a = {5, 0.25}