a+(a+1)+(a+2)+(a+3)+(a+4)+(a+5)+(a+6)=6(a+6)

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Solution for a+(a+1)+(a+2)+(a+3)+(a+4)+(a+5)+(a+6)=6(a+6) equation:


Simplifying
a + (a + 1) + (a + 2) + (a + 3) + (a + 4) + (a + 5) + (a + 6) = 6(a + 6)

Reorder the terms:
a + (1 + a) + (a + 2) + (a + 3) + (a + 4) + (a + 5) + (a + 6) = 6(a + 6)

Remove parenthesis around (1 + a)
a + 1 + a + (a + 2) + (a + 3) + (a + 4) + (a + 5) + (a + 6) = 6(a + 6)

Reorder the terms:
a + 1 + a + (2 + a) + (a + 3) + (a + 4) + (a + 5) + (a + 6) = 6(a + 6)

Remove parenthesis around (2 + a)
a + 1 + a + 2 + a + (a + 3) + (a + 4) + (a + 5) + (a + 6) = 6(a + 6)

Reorder the terms:
a + 1 + a + 2 + a + (3 + a) + (a + 4) + (a + 5) + (a + 6) = 6(a + 6)

Remove parenthesis around (3 + a)
a + 1 + a + 2 + a + 3 + a + (a + 4) + (a + 5) + (a + 6) = 6(a + 6)

Reorder the terms:
a + 1 + a + 2 + a + 3 + a + (4 + a) + (a + 5) + (a + 6) = 6(a + 6)

Remove parenthesis around (4 + a)
a + 1 + a + 2 + a + 3 + a + 4 + a + (a + 5) + (a + 6) = 6(a + 6)

Reorder the terms:
a + 1 + a + 2 + a + 3 + a + 4 + a + (5 + a) + (a + 6) = 6(a + 6)

Remove parenthesis around (5 + a)
a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + (a + 6) = 6(a + 6)

Reorder the terms:
a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + (6 + a) = 6(a + 6)

Remove parenthesis around (6 + a)
a + 1 + a + 2 + a + 3 + a + 4 + a + 5 + a + 6 + a = 6(a + 6)

Reorder the terms:
1 + 2 + 3 + 4 + 5 + 6 + a + a + a + a + a + a + a = 6(a + 6)

Combine like terms: 1 + 2 = 3
3 + 3 + 4 + 5 + 6 + a + a + a + a + a + a + a = 6(a + 6)

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

Combine like terms: 6 + 4 = 10
10 + 5 + 6 + a + a + a + a + a + a + a = 6(a + 6)

Combine like terms: 10 + 5 = 15
15 + 6 + a + a + a + a + a + a + a = 6(a + 6)

Combine like terms: 15 + 6 = 21
21 + a + a + a + a + a + a + a = 6(a + 6)

Combine like terms: a + a = 2a
21 + 2a + a + a + a + a + a = 6(a + 6)

Combine like terms: 2a + a = 3a
21 + 3a + a + a + a + a = 6(a + 6)

Combine like terms: 3a + a = 4a
21 + 4a + a + a + a = 6(a + 6)

Combine like terms: 4a + a = 5a
21 + 5a + a + a = 6(a + 6)

Combine like terms: 5a + a = 6a
21 + 6a + a = 6(a + 6)

Combine like terms: 6a + a = 7a
21 + 7a = 6(a + 6)

Reorder the terms:
21 + 7a = 6(6 + a)
21 + 7a = (6 * 6 + a * 6)
21 + 7a = (36 + 6a)

Solving
21 + 7a = 36 + 6a

Solving for variable 'a'.

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

Add '-6a' to each side of the equation.
21 + 7a + -6a = 36 + 6a + -6a

Combine like terms: 7a + -6a = 1a
21 + 1a = 36 + 6a + -6a

Combine like terms: 6a + -6a = 0
21 + 1a = 36 + 0
21 + 1a = 36

Add '-21' to each side of the equation.
21 + -21 + 1a = 36 + -21

Combine like terms: 21 + -21 = 0
0 + 1a = 36 + -21
1a = 36 + -21

Combine like terms: 36 + -21 = 15
1a = 15

Divide each side by '1'.
a = 15

Simplifying
a = 15

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