(3w-7)(4-w)=0

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Solution for (3w-7)(4-w)=0 equation: 


Simplifying
(3w + -7)(4 + -1w) = 0

Reorder the terms:
(-7 + 3w)(4 + -1w) = 0

Multiply (-7 + 3w) * (4 + -1w)
(-7(4 + -1w) + 3w * (4 + -1w)) = 0
((4 * -7 + -1w * -7) + 3w * (4 + -1w)) = 0
((-28 + 7w) + 3w * (4 + -1w)) = 0
(-28 + 7w + (4 * 3w + -1w * 3w)) = 0
(-28 + 7w + (12w + -3w2)) = 0

Combine like terms: 7w + 12w = 19w
(-28 + 19w + -3w2) = 0

Solving
-28 + 19w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + w)(7 + -3w) = 0


Subproblem 1
Set the factor '(-4 + w)' equal to zero and attempt to solve:

Simplifying
-4 + w = 0

Solving
-4 + w = 0

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

Add '4' to each side of the equation.
-4 + 4 + w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + w = 0 + 4
w = 0 + 4

Combine like terms: 0 + 4 = 4
w = 4

Simplifying
w = 4

Subproblem 2
Set the factor '(7 + -3w)' equal to zero and attempt to solve:

Simplifying
7 + -3w = 0

Solving
7 + -3w = 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 + -3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3w = 0 + -7
-3w = 0 + -7

Combine like terms: 0 + -7 = -7
-3w = -7

Divide each side by '-3'.
w = 2.333333333

Simplifying
w = 2.333333333
Solution
w = {4, 2.333333333}

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