(3w-5)(7-w)=0

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Solution for (3w-5)(7-w)=0 equation: 


Simplifying
(3w + -5)(7 + -1w) = 0

Reorder the terms:
(-5 + 3w)(7 + -1w) = 0

Multiply (-5 + 3w) * (7 + -1w)
(-5(7 + -1w) + 3w * (7 + -1w)) = 0
((7 * -5 + -1w * -5) + 3w * (7 + -1w)) = 0
((-35 + 5w) + 3w * (7 + -1w)) = 0
(-35 + 5w + (7 * 3w + -1w * 3w)) = 0
(-35 + 5w + (21w + -3w2)) = 0

Combine like terms: 5w + 21w = 26w
(-35 + 26w + -3w2) = 0

Solving
-35 + 26w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + w)(5 + -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 '(5 + -3w)' equal to zero and attempt to solve:

Simplifying
5 + -3w = 0

Solving
5 + -3w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3w = 0 + -5
-3w = 0 + -5

Combine like terms: 0 + -5 = -5
-3w = -5

Divide each side by '-3'.
w = 1.666666667

Simplifying
w = 1.666666667
Solution
w = {7, 1.666666667}

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