w(2w-7)(3w+8)=0

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Solution for w(2w-7)(3w+8)=0 equation: 


Simplifying
w(2w + -7)(3w + 8) = 0

Reorder the terms:
w(-7 + 2w)(3w + 8) = 0

Reorder the terms:
w(-7 + 2w)(8 + 3w) = 0

Multiply (-7 + 2w) * (8 + 3w)
w(-7(8 + 3w) + 2w * (8 + 3w)) = 0
w((8 * -7 + 3w * -7) + 2w * (8 + 3w)) = 0
w((-56 + -21w) + 2w * (8 + 3w)) = 0
w(-56 + -21w + (8 * 2w + 3w * 2w)) = 0
w(-56 + -21w + (16w + 6w2)) = 0

Combine like terms: -21w + 16w = -5w
w(-56 + -5w + 6w2) = 0
(-56 * w + -5w * w + 6w2 * w) = 0
(-56w + -5w2 + 6w3) = 0

Solving
-56w + -5w2 + 6w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), 'w'.
w(-56 + -5w + 6w2) = 0

Factor a trinomial.
w((-8 + -3w)(7 + -2w)) = 0


Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0

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

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

Simplifying
7 + -2w = 0

Solving
7 + -2w = 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 + -2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2w = 0 + -7
-2w = 0 + -7

Combine like terms: 0 + -7 = -7
-2w = -7

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5
Solution
w = {0, -2.666666667, 3.5}

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