(a-3)(a-3)=(a-4)(a-5)

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Solution for (a-3)(a-3)=(a-4)(a-5) equation: 


Simplifying
(a + -3)(a + -3) = (a + -4)(a + -5)

Reorder the terms:
(-3 + a)(a + -3) = (a + -4)(a + -5)

Reorder the terms:
(-3 + a)(-3 + a) = (a + -4)(a + -5)

Multiply (-3 + a) * (-3 + a)
(-3(-3 + a) + a(-3 + a)) = (a + -4)(a + -5)
((-3 * -3 + a * -3) + a(-3 + a)) = (a + -4)(a + -5)
((9 + -3a) + a(-3 + a)) = (a + -4)(a + -5)
(9 + -3a + (-3 * a + a * a)) = (a + -4)(a + -5)
(9 + -3a + (-3a + a2)) = (a + -4)(a + -5)

Combine like terms: -3a + -3a = -6a
(9 + -6a + a2) = (a + -4)(a + -5)

Reorder the terms:
9 + -6a + a2 = (-4 + a)(a + -5)

Reorder the terms:
9 + -6a + a2 = (-4 + a)(-5 + a)

Multiply (-4 + a) * (-5 + a)
9 + -6a + a2 = (-4(-5 + a) + a(-5 + a))
9 + -6a + a2 = ((-5 * -4 + a * -4) + a(-5 + a))
9 + -6a + a2 = ((20 + -4a) + a(-5 + a))
9 + -6a + a2 = (20 + -4a + (-5 * a + a * a))
9 + -6a + a2 = (20 + -4a + (-5a + a2))

Combine like terms: -4a + -5a = -9a
9 + -6a + a2 = (20 + -9a + a2)

Add '-1a2' to each side of the equation.
9 + -6a + a2 + -1a2 = 20 + -9a + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
9 + -6a + 0 = 20 + -9a + a2 + -1a2
9 + -6a = 20 + -9a + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
9 + -6a = 20 + -9a + 0
9 + -6a = 20 + -9a

Solving
9 + -6a = 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.
9 + -6a + 9a = 20 + -9a + 9a

Combine like terms: -6a + 9a = 3a
9 + 3a = 20 + -9a + 9a

Combine like terms: -9a + 9a = 0
9 + 3a = 20 + 0
9 + 3a = 20

Add '-9' to each side of the equation.
9 + -9 + 3a = 20 + -9

Combine like terms: 9 + -9 = 0
0 + 3a = 20 + -9
3a = 20 + -9

Combine like terms: 20 + -9 = 11
3a = 11

Divide each side by '3'.
a = 3.666666667

Simplifying
a = 3.666666667

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