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

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


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

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

Multiply (-2 + 3w) * (7 + -1w)
(-2(7 + -1w) + 3w * (7 + -1w)) = 0
((7 * -2 + -1w * -2) + 3w * (7 + -1w)) = 0
((-14 + 2w) + 3w * (7 + -1w)) = 0
(-14 + 2w + (7 * 3w + -1w * 3w)) = 0
(-14 + 2w + (21w + -3w2)) = 0

Combine like terms: 2w + 21w = 23w
(-14 + 23w + -3w2) = 0

Solving
-14 + 23w + -3w2 = 0

Solving for variable 'w'.

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


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 + -3w)' equal to zero and attempt to solve:

Simplifying
2 + -3w = 0

Solving
2 + -3w = 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 + -3w = 0 + -2

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

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

Divide each side by '-3'.
w = 0.6666666667

Simplifying
w = 0.6666666667
Solution
w = {7, 0.6666666667}

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