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

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

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

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

Reorder the terms:
-4 + 2a = 4a(-4 + 2a)
-4 + 2a = (-4 * 4a + 2a * 4a)
-4 + 2a = (-16a + 8a2)

Solving
-4 + 2a = -16a + 8a2

Solving for variable 'a'.

Combine like terms: 2a + 16a = 18a
-4 + 18a + -8a2 = -16a + 8a2 + 16a + -8a2

Reorder the terms:
-4 + 18a + -8a2 = -16a + 16a + 8a2 + -8a2

Combine like terms: -16a + 16a = 0
-4 + 18a + -8a2 = 0 + 8a2 + -8a2
-4 + 18a + -8a2 = 8a2 + -8a2

Combine like terms: 8a2 + -8a2 = 0
-4 + 18a + -8a2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 9a + -4a2) = 0

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

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

Simplifying
-2 + a = 0

Solving
-2 + a = 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 + a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + a = 0 + 2
a = 0 + 2

Combine like terms: 0 + 2 = 2
a = 2

Simplifying
a = 2
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 = {2, 0.25}