6-3w=3w(-w+5)-6(2w-5)

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Solution for 6-3w=3w(-w+5)-6(2w-5) equation: 


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

Reorder the terms:
6 + -3w = 3w(5 + -1w) + -6(2w + -5)
6 + -3w = (5 * 3w + -1w * 3w) + -6(2w + -5)
6 + -3w = (15w + -3w2) + -6(2w + -5)

Reorder the terms:
6 + -3w = 15w + -3w2 + -6(-5 + 2w)
6 + -3w = 15w + -3w2 + (-5 * -6 + 2w * -6)
6 + -3w = 15w + -3w2 + (30 + -12w)

Reorder the terms:
6 + -3w = 30 + 15w + -12w + -3w2

Combine like terms: 15w + -12w = 3w
6 + -3w = 30 + 3w + -3w2

Solving
6 + -3w = 30 + 3w + -3w2

Solving for variable 'w'.

Reorder the terms:
6 + -30 + -3w + -3w + 3w2 = 30 + 3w + -3w2 + -30 + -3w + 3w2

Combine like terms: 6 + -30 = -24
-24 + -3w + -3w + 3w2 = 30 + 3w + -3w2 + -30 + -3w + 3w2

Combine like terms: -3w + -3w = -6w
-24 + -6w + 3w2 = 30 + 3w + -3w2 + -30 + -3w + 3w2

Reorder the terms:
-24 + -6w + 3w2 = 30 + -30 + 3w + -3w + -3w2 + 3w2

Combine like terms: 30 + -30 = 0
-24 + -6w + 3w2 = 0 + 3w + -3w + -3w2 + 3w2
-24 + -6w + 3w2 = 3w + -3w + -3w2 + 3w2

Combine like terms: 3w + -3w = 0
-24 + -6w + 3w2 = 0 + -3w2 + 3w2
-24 + -6w + 3w2 = -3w2 + 3w2

Combine like terms: -3w2 + 3w2 = 0
-24 + -6w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2w + w2) = 0

Factor a trinomial.
3((-2 + -1w)(4 + -1w)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-2 + -1w)' equal to zero and attempt to solve:

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

Simplifying
w = -2

Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {-2, 4}

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