3(2a+1)+4(2-2a)=(a-2)(a+2)-(8a+a^2)+a+4(a-1)

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Solution for 3(2a+1)+4(2-2a)=(a-2)(a+2)-(8a+a^2)+a+4(a-1) equation: 


Simplifying
3(2a + 1) + 4(2 + -2a) = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)

Reorder the terms:
3(1 + 2a) + 4(2 + -2a) = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)
(1 * 3 + 2a * 3) + 4(2 + -2a) = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)
(3 + 6a) + 4(2 + -2a) = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)
3 + 6a + (2 * 4 + -2a * 4) = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)
3 + 6a + (8 + -8a) = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)

Reorder the terms:
3 + 8 + 6a + -8a = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)

Combine like terms: 3 + 8 = 11
11 + 6a + -8a = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)

Combine like terms: 6a + -8a = -2a
11 + -2a = (a + -2)(a + 2) + -1(8a + a2) + a + 4(a + -1)

Reorder the terms:
11 + -2a = (-2 + a)(a + 2) + -1(8a + a2) + a + 4(a + -1)

Reorder the terms:
11 + -2a = (-2 + a)(2 + a) + -1(8a + a2) + a + 4(a + -1)

Multiply (-2 + a) * (2 + a)
11 + -2a = (-2(2 + a) + a(2 + a)) + -1(8a + a2) + a + 4(a + -1)
11 + -2a = ((2 * -2 + a * -2) + a(2 + a)) + -1(8a + a2) + a + 4(a + -1)
11 + -2a = ((-4 + -2a) + a(2 + a)) + -1(8a + a2) + a + 4(a + -1)
11 + -2a = (-4 + -2a + (2 * a + a * a)) + -1(8a + a2) + a + 4(a + -1)
11 + -2a = (-4 + -2a + (2a + a2)) + -1(8a + a2) + a + 4(a + -1)

Combine like terms: -2a + 2a = 0
11 + -2a = (-4 + 0 + a2) + -1(8a + a2) + a + 4(a + -1)
11 + -2a = (-4 + a2) + -1(8a + a2) + a + 4(a + -1)
11 + -2a = -4 + a2 + (8a * -1 + a2 * -1) + a + 4(a + -1)
11 + -2a = -4 + a2 + (-8a + -1a2) + a + 4(a + -1)

Reorder the terms:
11 + -2a = -4 + a2 + -8a + -1a2 + a + 4(-1 + a)
11 + -2a = -4 + a2 + -8a + -1a2 + a + (-1 * 4 + a * 4)
11 + -2a = -4 + a2 + -8a + -1a2 + a + (-4 + 4a)

Reorder the terms:
11 + -2a = -4 + -4 + -8a + a + 4a + a2 + -1a2

Combine like terms: -4 + -4 = -8
11 + -2a = -8 + -8a + a + 4a + a2 + -1a2

Combine like terms: -8a + a = -7a
11 + -2a = -8 + -7a + 4a + a2 + -1a2

Combine like terms: -7a + 4a = -3a
11 + -2a = -8 + -3a + a2 + -1a2

Combine like terms: a2 + -1a2 = 0
11 + -2a = -8 + -3a + 0
11 + -2a = -8 + -3a

Solving
11 + -2a = -8 + -3a

Solving for variable 'a'.

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

Add '3a' to each side of the equation.
11 + -2a + 3a = -8 + -3a + 3a

Combine like terms: -2a + 3a = 1a
11 + 1a = -8 + -3a + 3a

Combine like terms: -3a + 3a = 0
11 + 1a = -8 + 0
11 + 1a = -8

Add '-11' to each side of the equation.
11 + -11 + 1a = -8 + -11

Combine like terms: 11 + -11 = 0
0 + 1a = -8 + -11
1a = -8 + -11

Combine like terms: -8 + -11 = -19
1a = -19

Divide each side by '1'.
a = -19

Simplifying
a = -19

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