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

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


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

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

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

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

Combine like terms: -28w + -9w = -37w
6x(63 + -37w + 4w2) = 0
(63 * 6x + -37w * 6x + 4w2 * 6x) = 0

Reorder the terms:
(-222wx + 24w2x + 378x) = 0
(-222wx + 24w2x + 378x) = 0

Solving
-222wx + 24w2x + 378x = 0

Solving for variable 'w'.

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

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

Ignore the factor 6.

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

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
w + -7 = 0

Reorder the terms:
-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 3
Set the factor '(4w + -9)' equal to zero and attempt to solve:

Simplifying
4w + -9 = 0

Reorder the terms:
-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
Solution
w = {7, 2.25}

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