x(4x-3)(7-9x)=0

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Solution for x(4x-3)(7-9x)=0 equation: 


Simplifying
x(4x + -3)(7 + -9x) = 0

Reorder the terms:
x(-3 + 4x)(7 + -9x) = 0

Multiply (-3 + 4x) * (7 + -9x)
x(-3(7 + -9x) + 4x * (7 + -9x)) = 0
x((7 * -3 + -9x * -3) + 4x * (7 + -9x)) = 0
x((-21 + 27x) + 4x * (7 + -9x)) = 0
x(-21 + 27x + (7 * 4x + -9x * 4x)) = 0
x(-21 + 27x + (28x + -36x2)) = 0

Combine like terms: 27x + 28x = 55x
x(-21 + 55x + -36x2) = 0
(-21 * x + 55x * x + -36x2 * x) = 0
(-21x + 55x2 + -36x3) = 0

Solving
-21x + 55x2 + -36x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-21 + 55x + -36x2) = 0

Factor a trinomial.
x((-7 + 9x)(3 + -4x)) = 0


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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-7 + 9x)' equal to zero and attempt to solve:

Simplifying
-7 + 9x = 0

Solving
-7 + 9x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 9x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 9x = 0 + 7
9x = 0 + 7

Combine like terms: 0 + 7 = 7
9x = 7

Divide each side by '9'.
x = 0.7777777778

Simplifying
x = 0.7777777778

Subproblem 3
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {0, 0.7777777778, 0.75}

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