(7+w)(3w-8)=0

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Solution for (7+w)(3w-8)=0 equation: 


Simplifying
(7 + w)(3w + -8) = 0

Reorder the terms:
(7 + w)(-8 + 3w) = 0

Multiply (7 + w) * (-8 + 3w)
(7(-8 + 3w) + w(-8 + 3w)) = 0
((-8 * 7 + 3w * 7) + w(-8 + 3w)) = 0
((-56 + 21w) + w(-8 + 3w)) = 0
(-56 + 21w + (-8 * w + 3w * w)) = 0
(-56 + 21w + (-8w + 3w2)) = 0

Combine like terms: 21w + -8w = 13w
(-56 + 13w + 3w2) = 0

Solving
-56 + 13w + 3w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -1w)(8 + -3w) = 0


Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve:

Simplifying
-7 + -1w = 0

Solving
-7 + -1w = 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 + -1w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1w = 0 + 7
-1w = 0 + 7

Combine like terms: 0 + 7 = 7
-1w = 7

Divide each side by '-1'.
w = -7

Simplifying
w = -7

Subproblem 2
Set the factor '(8 + -3w)' equal to zero and attempt to solve:

Simplifying
8 + -3w = 0

Solving
8 + -3w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3w = 0 + -8
-3w = 0 + -8

Combine like terms: 0 + -8 = -8
-3w = -8

Divide each side by '-3'.
w = 2.666666667

Simplifying
w = 2.666666667
Solution
w = {-7, 2.666666667}

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