(2a-6)(a-2)-(a-3)(2a-2)=

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Solution for (2a-6)(a-2)-(a-3)(2a-2)= equation: 


Simplifying
(2a + -6)(a + -2) + -1(a + -3)(2a + -2) = 0

Reorder the terms:
(-6 + 2a)(a + -2) + -1(a + -3)(2a + -2) = 0

Reorder the terms:
(-6 + 2a)(-2 + a) + -1(a + -3)(2a + -2) = 0

Multiply (-6 + 2a) * (-2 + a)
(-6(-2 + a) + 2a * (-2 + a)) + -1(a + -3)(2a + -2) = 0
((-2 * -6 + a * -6) + 2a * (-2 + a)) + -1(a + -3)(2a + -2) = 0
((12 + -6a) + 2a * (-2 + a)) + -1(a + -3)(2a + -2) = 0
(12 + -6a + (-2 * 2a + a * 2a)) + -1(a + -3)(2a + -2) = 0
(12 + -6a + (-4a + 2a2)) + -1(a + -3)(2a + -2) = 0

Combine like terms: -6a + -4a = -10a
(12 + -10a + 2a2) + -1(a + -3)(2a + -2) = 0

Reorder the terms:
12 + -10a + 2a2 + -1(-3 + a)(2a + -2) = 0

Reorder the terms:
12 + -10a + 2a2 + -1(-3 + a)(-2 + 2a) = 0

Multiply (-3 + a) * (-2 + 2a)
12 + -10a + 2a2 + -1(-3(-2 + 2a) + a(-2 + 2a)) = 0
12 + -10a + 2a2 + -1((-2 * -3 + 2a * -3) + a(-2 + 2a)) = 0
12 + -10a + 2a2 + -1((6 + -6a) + a(-2 + 2a)) = 0
12 + -10a + 2a2 + -1(6 + -6a + (-2 * a + 2a * a)) = 0
12 + -10a + 2a2 + -1(6 + -6a + (-2a + 2a2)) = 0

Combine like terms: -6a + -2a = -8a
12 + -10a + 2a2 + -1(6 + -8a + 2a2) = 0
12 + -10a + 2a2 + (6 * -1 + -8a * -1 + 2a2 * -1) = 0
12 + -10a + 2a2 + (-6 + 8a + -2a2) = 0

Reorder the terms:
12 + -6 + -10a + 8a + 2a2 + -2a2 = 0

Combine like terms: 12 + -6 = 6
6 + -10a + 8a + 2a2 + -2a2 = 0

Combine like terms: -10a + 8a = -2a
6 + -2a + 2a2 + -2a2 = 0

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

Solving
6 + -2a = 0

Solving for variable 'a'.

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

Add '-6' to each side of the equation.
6 + -6 + -2a = 0 + -6

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

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

Divide each side by '-2'.
a = 3

Simplifying
a = 3

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