-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 = -5w
-3(14 + -5w + -1w2) = 0
(14 * -3 + -5w * -3 + -1w2 * -3) = 0
(-42 + 15w + 3w2) = 0

Solving
-42 + 15w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5w + w2) = 0

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

Ignore the factor 3.

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

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 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 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
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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