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

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


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

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

Multiply (3 + w) * (-7 + 4w)
(3(-7 + 4w) + w(-7 + 4w)) = 0
((-7 * 3 + 4w * 3) + w(-7 + 4w)) = 0
((-21 + 12w) + w(-7 + 4w)) = 0
(-21 + 12w + (-7 * w + 4w * w)) = 0
(-21 + 12w + (-7w + 4w2)) = 0

Combine like terms: 12w + -7w = 5w
(-21 + 5w + 4w2) = 0

Solving
-21 + 5w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(7 + -4w) = 0


Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 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 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3

Subproblem 2
Set the factor '(7 + -4w)' equal to zero and attempt to solve:

Simplifying
7 + -4w = 0

Solving
7 + -4w = 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 + -4w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4w = 0 + -7
-4w = 0 + -7

Combine like terms: 0 + -7 = -7
-4w = -7

Divide each side by '-4'.
w = 1.75

Simplifying
w = 1.75
Solution
w = {-3, 1.75}

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