6w(w-7)(4w-9)=0

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Solution for 6w(w-7)(4w-9)=0 equation: 


Simplifying
6w(w + -7)(4w + -9) = 0

Reorder the terms:
6w(-7 + w)(4w + -9) = 0

Reorder the terms:
6w(-7 + w)(-9 + 4w) = 0

Multiply (-7 + w) * (-9 + 4w)
6w(-7(-9 + 4w) + w(-9 + 4w)) = 0
6w((-9 * -7 + 4w * -7) + w(-9 + 4w)) = 0
6w((63 + -28w) + w(-9 + 4w)) = 0
6w(63 + -28w + (-9 * w + 4w * w)) = 0
6w(63 + -28w + (-9w + 4w2)) = 0

Combine like terms: -28w + -9w = -37w
6w(63 + -37w + 4w2) = 0
(63 * 6w + -37w * 6w + 4w2 * 6w) = 0
(378w + -222w2 + 24w3) = 0

Solving
378w + -222w2 + 24w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6w'.
6w(63 + -37w + 4w2) = 0

Factor a trinomial.
6w((9 + -4w)(7 + -1w)) = 0

Ignore the factor 6.

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 '(9 + -4w)' equal to zero and attempt to solve:

Simplifying
9 + -4w = 0

Solving
9 + -4w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4w = 0 + -9
-4w = 0 + -9

Combine like terms: 0 + -9 = -9
-4w = -9

Divide each side by '-4'.
w = 2.25

Simplifying
w = 2.25

Subproblem 3
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
Solution
w = {0, 2.25, 7}

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