(a-2)*(a-2)=(a-4)(a-5)

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Solution for (a-2)*(a-2)=(a-4)(a-5) equation: 


Simplifying
(a + -2)(a + -2) = (a + -4)(a + -5)

Reorder the terms:
(-2 + a)(a + -2) = (a + -4)(a + -5)

Reorder the terms:
(-2 + a)(-2 + a) = (a + -4)(a + -5)

Multiply (-2 + a) * (-2 + a)
(-2(-2 + a) + a(-2 + a)) = (a + -4)(a + -5)
((-2 * -2 + a * -2) + a(-2 + a)) = (a + -4)(a + -5)
((4 + -2a) + a(-2 + a)) = (a + -4)(a + -5)
(4 + -2a + (-2 * a + a * a)) = (a + -4)(a + -5)
(4 + -2a + (-2a + a2)) = (a + -4)(a + -5)

Combine like terms: -2a + -2a = -4a
(4 + -4a + a2) = (a + -4)(a + -5)

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

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

Multiply (-4 + a) * (-5 + a)
4 + -4a + a2 = (-4(-5 + a) + a(-5 + a))
4 + -4a + a2 = ((-5 * -4 + a * -4) + a(-5 + a))
4 + -4a + a2 = ((20 + -4a) + a(-5 + a))
4 + -4a + a2 = (20 + -4a + (-5 * a + a * a))
4 + -4a + a2 = (20 + -4a + (-5a + a2))

Combine like terms: -4a + -5a = -9a
4 + -4a + a2 = (20 + -9a + a2)

Add '-1a2' to each side of the equation.
4 + -4a + a2 + -1a2 = 20 + -9a + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
4 + -4a + 0 = 20 + -9a + a2 + -1a2
4 + -4a = 20 + -9a + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
4 + -4a = 20 + -9a + 0
4 + -4a = 20 + -9a

Solving
4 + -4a = 20 + -9a

Solving for variable 'a'.

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

Add '9a' to each side of the equation.
4 + -4a + 9a = 20 + -9a + 9a

Combine like terms: -4a + 9a = 5a
4 + 5a = 20 + -9a + 9a

Combine like terms: -9a + 9a = 0
4 + 5a = 20 + 0
4 + 5a = 20

Add '-4' to each side of the equation.
4 + -4 + 5a = 20 + -4

Combine like terms: 4 + -4 = 0
0 + 5a = 20 + -4
5a = 20 + -4

Combine like terms: 20 + -4 = 16
5a = 16

Divide each side by '5'.
a = 3.2

Simplifying
a = 3.2

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