3(w-2)(-w+7)=0

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Solution for 3(w-2)(-w+7)=0 equation: 


Simplifying
3(w + -2)(-1w + 7) = 0

Reorder the terms:
3(-2 + w)(-1w + 7) = 0

Reorder the terms:
3(-2 + w)(7 + -1w) = 0

Multiply (-2 + w) * (7 + -1w)
3(-2(7 + -1w) + w(7 + -1w)) = 0
3((7 * -2 + -1w * -2) + w(7 + -1w)) = 0
3((-14 + 2w) + w(7 + -1w)) = 0
3(-14 + 2w + (7 * w + -1w * w)) = 0
3(-14 + 2w + (7w + -1w2)) = 0

Combine like terms: 2w + 7w = 9w
3(-14 + 9w + -1w2) = 0
(-14 * 3 + 9w * 3 + -1w2 * 3) = 0
(-42 + 27w + -3w2) = 0

Solving
-42 + 27w + -3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 9w + -1w2) = 0

Factor a trinomial.
3((-7 + w)(2 + -1w)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + w)' equal to zero and attempt to solve:

Simplifying
-7 + w = 0

Solving
-7 + w = 0

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

Add '7' to each side of the equation.
-7 + 7 + w = 0 + 7

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

Combine like terms: 0 + 7 = 7
w = 7

Simplifying
w = 7

Subproblem 2
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
Solution
w = {7, 2}

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