(a)(a)+(a+8)(a+8)=(a+16)(a+16)

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Solution for (a)(a)+(a+8)(a+8)=(a+16)(a+16) equation: 


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

Multiply a * a
a2 + (a + 8)(a + 8) = (a + 16)(a + 16)

Reorder the terms:
a2 + (8 + a)(a + 8) = (a + 16)(a + 16)

Reorder the terms:
a2 + (8 + a)(8 + a) = (a + 16)(a + 16)

Multiply (8 + a) * (8 + a)
a2 + (8(8 + a) + a(8 + a)) = (a + 16)(a + 16)
a2 + ((8 * 8 + a * 8) + a(8 + a)) = (a + 16)(a + 16)
a2 + ((64 + 8a) + a(8 + a)) = (a + 16)(a + 16)
a2 + (64 + 8a + (8 * a + a * a)) = (a + 16)(a + 16)
a2 + (64 + 8a + (8a + a2)) = (a + 16)(a + 16)

Combine like terms: 8a + 8a = 16a
a2 + (64 + 16a + a2) = (a + 16)(a + 16)

Reorder the terms:
64 + 16a + a2 + a2 = (a + 16)(a + 16)

Combine like terms: a2 + a2 = 2a2
64 + 16a + 2a2 = (a + 16)(a + 16)

Reorder the terms:
64 + 16a + 2a2 = (16 + a)(a + 16)

Reorder the terms:
64 + 16a + 2a2 = (16 + a)(16 + a)

Multiply (16 + a) * (16 + a)
64 + 16a + 2a2 = (16(16 + a) + a(16 + a))
64 + 16a + 2a2 = ((16 * 16 + a * 16) + a(16 + a))
64 + 16a + 2a2 = ((256 + 16a) + a(16 + a))
64 + 16a + 2a2 = (256 + 16a + (16 * a + a * a))
64 + 16a + 2a2 = (256 + 16a + (16a + a2))

Combine like terms: 16a + 16a = 32a
64 + 16a + 2a2 = (256 + 32a + a2)

Solving
64 + 16a + 2a2 = 256 + 32a + a2

Solving for variable 'a'.

Reorder the terms:
64 + -256 + 16a + -32a + 2a2 + -1a2 = 256 + 32a + a2 + -256 + -32a + -1a2

Combine like terms: 64 + -256 = -192
-192 + 16a + -32a + 2a2 + -1a2 = 256 + 32a + a2 + -256 + -32a + -1a2

Combine like terms: 16a + -32a = -16a
-192 + -16a + 2a2 + -1a2 = 256 + 32a + a2 + -256 + -32a + -1a2

Combine like terms: 2a2 + -1a2 = 1a2
-192 + -16a + 1a2 = 256 + 32a + a2 + -256 + -32a + -1a2

Reorder the terms:
-192 + -16a + 1a2 = 256 + -256 + 32a + -32a + a2 + -1a2

Combine like terms: 256 + -256 = 0
-192 + -16a + 1a2 = 0 + 32a + -32a + a2 + -1a2
-192 + -16a + 1a2 = 32a + -32a + a2 + -1a2

Combine like terms: 32a + -32a = 0
-192 + -16a + 1a2 = 0 + a2 + -1a2
-192 + -16a + 1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-192 + -16a + 1a2 = 0

Factor a trinomial.
(-8 + -1a)(24 + -1a) = 0


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

Simplifying
-8 + -1a = 0

Solving
-8 + -1a = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1a = 0 + 8

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

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

Divide each side by '-1'.
a = -8

Simplifying
a = -8

Subproblem 2
Set the factor '(24 + -1a)' equal to zero and attempt to solve:

Simplifying
24 + -1a = 0

Solving
24 + -1a = 0

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

Add '-24' to each side of the equation.
24 + -24 + -1a = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -1a = 0 + -24
-1a = 0 + -24

Combine like terms: 0 + -24 = -24
-1a = -24

Divide each side by '-1'.
a = 24

Simplifying
a = 24
Solution
a = {-8, 24}

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