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

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


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

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

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

Combine like terms: 3w + 14w = 17w
(-21 + 17w + -2w2) = 0

Solving
-21 + 17w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + w)(3 + -2w) = 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 '(3 + -2w)' equal to zero and attempt to solve:

Simplifying
3 + -2w = 0

Solving
3 + -2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2w = 0 + -3

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

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

Divide each side by '-2'.
w = 1.5

Simplifying
w = 1.5
Solution
w = {7, 1.5}

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