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

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


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

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

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

Combine like terms: 21w + 5w = 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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