7(3w+1)-9(1+2w)=-2(w+4)-(4w-5)+6

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Solution for 7(3w+1)-9(1+2w)=-2(w+4)-(4w-5)+6 equation: 


Simplifying
7(3w + 1) + -9(1 + 2w) = -2(w + 4) + -1(4w + -5) + 6

Reorder the terms:
7(1 + 3w) + -9(1 + 2w) = -2(w + 4) + -1(4w + -5) + 6
(1 * 7 + 3w * 7) + -9(1 + 2w) = -2(w + 4) + -1(4w + -5) + 6
(7 + 21w) + -9(1 + 2w) = -2(w + 4) + -1(4w + -5) + 6
7 + 21w + (1 * -9 + 2w * -9) = -2(w + 4) + -1(4w + -5) + 6
7 + 21w + (-9 + -18w) = -2(w + 4) + -1(4w + -5) + 6

Reorder the terms:
7 + -9 + 21w + -18w = -2(w + 4) + -1(4w + -5) + 6

Combine like terms: 7 + -9 = -2
-2 + 21w + -18w = -2(w + 4) + -1(4w + -5) + 6

Combine like terms: 21w + -18w = 3w
-2 + 3w = -2(w + 4) + -1(4w + -5) + 6

Reorder the terms:
-2 + 3w = -2(4 + w) + -1(4w + -5) + 6
-2 + 3w = (4 * -2 + w * -2) + -1(4w + -5) + 6
-2 + 3w = (-8 + -2w) + -1(4w + -5) + 6

Reorder the terms:
-2 + 3w = -8 + -2w + -1(-5 + 4w) + 6
-2 + 3w = -8 + -2w + (-5 * -1 + 4w * -1) + 6
-2 + 3w = -8 + -2w + (5 + -4w) + 6

Reorder the terms:
-2 + 3w = -8 + 5 + 6 + -2w + -4w

Combine like terms: -8 + 5 = -3
-2 + 3w = -3 + 6 + -2w + -4w

Combine like terms: -3 + 6 = 3
-2 + 3w = 3 + -2w + -4w

Combine like terms: -2w + -4w = -6w
-2 + 3w = 3 + -6w

Solving
-2 + 3w = 3 + -6w

Solving for variable 'w'.

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

Add '6w' to each side of the equation.
-2 + 3w + 6w = 3 + -6w + 6w

Combine like terms: 3w + 6w = 9w
-2 + 9w = 3 + -6w + 6w

Combine like terms: -6w + 6w = 0
-2 + 9w = 3 + 0
-2 + 9w = 3

Add '2' to each side of the equation.
-2 + 2 + 9w = 3 + 2

Combine like terms: -2 + 2 = 0
0 + 9w = 3 + 2
9w = 3 + 2

Combine like terms: 3 + 2 = 5
9w = 5

Divide each side by '9'.
w = 0.5555555556

Simplifying
w = 0.5555555556

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