(w-3)-5(w+7)=10(w+3)-(7w+5)

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Solution for (w-3)-5(w+7)=10(w+3)-(7w+5) equation:


Simplifying
(w + -3) + -5(w + 7) = 10(w + 3) + -1(7w + 5)

Reorder the terms:
(-3 + w) + -5(w + 7) = 10(w + 3) + -1(7w + 5)

Remove parenthesis around (-3 + w)
-3 + w + -5(w + 7) = 10(w + 3) + -1(7w + 5)

Reorder the terms:
-3 + w + -5(7 + w) = 10(w + 3) + -1(7w + 5)
-3 + w + (7 * -5 + w * -5) = 10(w + 3) + -1(7w + 5)
-3 + w + (-35 + -5w) = 10(w + 3) + -1(7w + 5)

Reorder the terms:
-3 + -35 + w + -5w = 10(w + 3) + -1(7w + 5)

Combine like terms: -3 + -35 = -38
-38 + w + -5w = 10(w + 3) + -1(7w + 5)

Combine like terms: w + -5w = -4w
-38 + -4w = 10(w + 3) + -1(7w + 5)

Reorder the terms:
-38 + -4w = 10(3 + w) + -1(7w + 5)
-38 + -4w = (3 * 10 + w * 10) + -1(7w + 5)
-38 + -4w = (30 + 10w) + -1(7w + 5)

Reorder the terms:
-38 + -4w = 30 + 10w + -1(5 + 7w)
-38 + -4w = 30 + 10w + (5 * -1 + 7w * -1)
-38 + -4w = 30 + 10w + (-5 + -7w)

Reorder the terms:
-38 + -4w = 30 + -5 + 10w + -7w

Combine like terms: 30 + -5 = 25
-38 + -4w = 25 + 10w + -7w

Combine like terms: 10w + -7w = 3w
-38 + -4w = 25 + 3w

Solving
-38 + -4w = 25 + 3w

Solving for variable 'w'.

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

Add '-3w' to each side of the equation.
-38 + -4w + -3w = 25 + 3w + -3w

Combine like terms: -4w + -3w = -7w
-38 + -7w = 25 + 3w + -3w

Combine like terms: 3w + -3w = 0
-38 + -7w = 25 + 0
-38 + -7w = 25

Add '38' to each side of the equation.
-38 + 38 + -7w = 25 + 38

Combine like terms: -38 + 38 = 0
0 + -7w = 25 + 38
-7w = 25 + 38

Combine like terms: 25 + 38 = 63
-7w = 63

Divide each side by '-7'.
w = -9

Simplifying
w = -9

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