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

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


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

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

Multiply (-4 + 3w) * (7 + -1w)
(-4(7 + -1w) + 3w * (7 + -1w)) = 0
((7 * -4 + -1w * -4) + 3w * (7 + -1w)) = 0
((-28 + 4w) + 3w * (7 + -1w)) = 0
(-28 + 4w + (7 * 3w + -1w * 3w)) = 0
(-28 + 4w + (21w + -3w2)) = 0

Combine like terms: 4w + 21w = 25w
(-28 + 25w + -3w2) = 0

Solving
-28 + 25w + -3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + w)(4 + -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 '(4 + -3w)' equal to zero and attempt to solve:

Simplifying
4 + -3w = 0

Solving
4 + -3w = 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 + -3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3w = 0 + -4
-3w = 0 + -4

Combine like terms: 0 + -4 = -4
-3w = -4

Divide each side by '-3'.
w = 1.333333333

Simplifying
w = 1.333333333
Solution
w = {7, 1.333333333}

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