(a-1)(a+1)-(a-4)(a-4)=5

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Solution for (a-1)(a+1)-(a-4)(a-4)=5 equation: 


Simplifying
(a + -1)(a + 1) + -1(a + -4)(a + -4) = 5

Reorder the terms:
(-1 + a)(a + 1) + -1(a + -4)(a + -4) = 5

Reorder the terms:
(-1 + a)(1 + a) + -1(a + -4)(a + -4) = 5

Multiply (-1 + a) * (1 + a)
(-1(1 + a) + a(1 + a)) + -1(a + -4)(a + -4) = 5
((1 * -1 + a * -1) + a(1 + a)) + -1(a + -4)(a + -4) = 5
((-1 + -1a) + a(1 + a)) + -1(a + -4)(a + -4) = 5
(-1 + -1a + (1 * a + a * a)) + -1(a + -4)(a + -4) = 5
(-1 + -1a + (1a + a2)) + -1(a + -4)(a + -4) = 5

Combine like terms: -1a + 1a = 0
(-1 + 0 + a2) + -1(a + -4)(a + -4) = 5
(-1 + a2) + -1(a + -4)(a + -4) = 5

Reorder the terms:
-1 + a2 + -1(-4 + a)(a + -4) = 5

Reorder the terms:
-1 + a2 + -1(-4 + a)(-4 + a) = 5

Multiply (-4 + a) * (-4 + a)
-1 + a2 + -1(-4(-4 + a) + a(-4 + a)) = 5
-1 + a2 + -1((-4 * -4 + a * -4) + a(-4 + a)) = 5
-1 + a2 + -1((16 + -4a) + a(-4 + a)) = 5
-1 + a2 + -1(16 + -4a + (-4 * a + a * a)) = 5
-1 + a2 + -1(16 + -4a + (-4a + a2)) = 5

Combine like terms: -4a + -4a = -8a
-1 + a2 + -1(16 + -8a + a2) = 5
-1 + a2 + (16 * -1 + -8a * -1 + a2 * -1) = 5
-1 + a2 + (-16 + 8a + -1a2) = 5

Reorder the terms:
-1 + -16 + 8a + a2 + -1a2 = 5

Combine like terms: -1 + -16 = -17
-17 + 8a + a2 + -1a2 = 5

Combine like terms: a2 + -1a2 = 0
-17 + 8a + 0 = 5
-17 + 8a = 5

Solving
-17 + 8a = 5

Solving for variable 'a'.

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

Add '17' to each side of the equation.
-17 + 17 + 8a = 5 + 17

Combine like terms: -17 + 17 = 0
0 + 8a = 5 + 17
8a = 5 + 17

Combine like terms: 5 + 17 = 22
8a = 22

Divide each side by '8'.
a = 2.75

Simplifying
a = 2.75

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