2(q-2)+6=7(q-1)-2(q-6)

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Solution for 2(q-2)+6=7(q-1)-2(q-6) equation:


Simplifying
2(q + -2) + 6 = 7(q + -1) + -2(q + -6)

Reorder the terms:
2(-2 + q) + 6 = 7(q + -1) + -2(q + -6)
(-2 * 2 + q * 2) + 6 = 7(q + -1) + -2(q + -6)
(-4 + 2q) + 6 = 7(q + -1) + -2(q + -6)

Reorder the terms:
-4 + 6 + 2q = 7(q + -1) + -2(q + -6)

Combine like terms: -4 + 6 = 2
2 + 2q = 7(q + -1) + -2(q + -6)

Reorder the terms:
2 + 2q = 7(-1 + q) + -2(q + -6)
2 + 2q = (-1 * 7 + q * 7) + -2(q + -6)
2 + 2q = (-7 + 7q) + -2(q + -6)

Reorder the terms:
2 + 2q = -7 + 7q + -2(-6 + q)
2 + 2q = -7 + 7q + (-6 * -2 + q * -2)
2 + 2q = -7 + 7q + (12 + -2q)

Reorder the terms:
2 + 2q = -7 + 12 + 7q + -2q

Combine like terms: -7 + 12 = 5
2 + 2q = 5 + 7q + -2q

Combine like terms: 7q + -2q = 5q
2 + 2q = 5 + 5q

Solving
2 + 2q = 5 + 5q

Solving for variable 'q'.

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

Add '-5q' to each side of the equation.
2 + 2q + -5q = 5 + 5q + -5q

Combine like terms: 2q + -5q = -3q
2 + -3q = 5 + 5q + -5q

Combine like terms: 5q + -5q = 0
2 + -3q = 5 + 0
2 + -3q = 5

Add '-2' to each side of the equation.
2 + -2 + -3q = 5 + -2

Combine like terms: 2 + -2 = 0
0 + -3q = 5 + -2
-3q = 5 + -2

Combine like terms: 5 + -2 = 3
-3q = 3

Divide each side by '-3'.
q = -1

Simplifying
q = -1

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