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

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


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

Reorder the terms:
(-2 + a)(a + -4) + (a + -2)(a + 4) = 0

Reorder the terms:
(-2 + a)(-4 + a) + (a + -2)(a + 4) = 0

Multiply (-2 + a) * (-4 + a)
(-2(-4 + a) + a(-4 + a)) + (a + -2)(a + 4) = 0
((-4 * -2 + a * -2) + a(-4 + a)) + (a + -2)(a + 4) = 0
((8 + -2a) + a(-4 + a)) + (a + -2)(a + 4) = 0
(8 + -2a + (-4 * a + a * a)) + (a + -2)(a + 4) = 0
(8 + -2a + (-4a + a2)) + (a + -2)(a + 4) = 0

Combine like terms: -2a + -4a = -6a
(8 + -6a + a2) + (a + -2)(a + 4) = 0

Reorder the terms:
8 + -6a + a2 + (-2 + a)(a + 4) = 0

Reorder the terms:
8 + -6a + a2 + (-2 + a)(4 + a) = 0

Multiply (-2 + a) * (4 + a)
8 + -6a + a2 + (-2(4 + a) + a(4 + a)) = 0
8 + -6a + a2 + ((4 * -2 + a * -2) + a(4 + a)) = 0
8 + -6a + a2 + ((-8 + -2a) + a(4 + a)) = 0
8 + -6a + a2 + (-8 + -2a + (4 * a + a * a)) = 0
8 + -6a + a2 + (-8 + -2a + (4a + a2)) = 0

Combine like terms: -2a + 4a = 2a
8 + -6a + a2 + (-8 + 2a + a2) = 0

Reorder the terms:
8 + -8 + -6a + 2a + a2 + a2 = 0

Combine like terms: 8 + -8 = 0
0 + -6a + 2a + a2 + a2 = 0
-6a + 2a + a2 + a2 = 0

Combine like terms: -6a + 2a = -4a
-4a + a2 + a2 = 0

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

Solving
-4a + 2a2 = 0

Solving for variable 'a'.

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

Ignore the factor 2.

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
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
Solution
a = {0, 2}

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