4(a-4)=8a(4a-16)

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Solution for 4(a-4)=8a(4a-16) equation: 


Simplifying
4(a + -4) = 8a(4a + -16)

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

Reorder the terms:
-16 + 4a = 8a(-16 + 4a)
-16 + 4a = (-16 * 8a + 4a * 8a)
-16 + 4a = (-128a + 32a2)

Solving
-16 + 4a = -128a + 32a2

Solving for variable 'a'.

Combine like terms: 4a + 128a = 132a
-16 + 132a + -32a2 = -128a + 32a2 + 128a + -32a2

Reorder the terms:
-16 + 132a + -32a2 = -128a + 128a + 32a2 + -32a2

Combine like terms: -128a + 128a = 0
-16 + 132a + -32a2 = 0 + 32a2 + -32a2
-16 + 132a + -32a2 = 32a2 + -32a2

Combine like terms: 32a2 + -32a2 = 0
-16 + 132a + -32a2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 33a + -8a2) = 0

Factor a trinomial.
4((-4 + a)(1 + -8a)) = 0

Ignore the factor 4.

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

Simplifying
-4 + a = 0

Solving
-4 + a = 0

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + a = 0 + 4

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

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

Simplifying
a = 4

Subproblem 2
Set the factor '(1 + -8a)' equal to zero and attempt to solve:

Simplifying
1 + -8a = 0

Solving
1 + -8a = 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 + -8a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -8a = 0 + -1
-8a = 0 + -1

Combine like terms: 0 + -1 = -1
-8a = -1

Divide each side by '-8'.
a = 0.125

Simplifying
a = 0.125
Solution
a = {4, 0.125}

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