=6(x^2-3x)(5x^2-15x+9)

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Solution for =6(x^2-3x)(5x^2-15x+9) equation: 


Simplifying
0 = 6(x2 + -3x)(5x2 + -15x + 9)

Reorder the terms:
0 = 6(-3x + x2)(5x2 + -15x + 9)

Reorder the terms:
0 = 6(-3x + x2)(9 + -15x + 5x2)

Multiply (-3x + x2) * (9 + -15x + 5x2)
0 = 6(-3x * (9 + -15x + 5x2) + x2(9 + -15x + 5x2))
0 = 6((9 * -3x + -15x * -3x + 5x2 * -3x) + x2(9 + -15x + 5x2))
0 = 6((-27x + 45x2 + -15x3) + x2(9 + -15x + 5x2))
0 = 6(-27x + 45x2 + -15x3 + (9 * x2 + -15x * x2 + 5x2 * x2))
0 = 6(-27x + 45x2 + -15x3 + (9x2 + -15x3 + 5x4))

Reorder the terms:
0 = 6(-27x + 45x2 + 9x2 + -15x3 + -15x3 + 5x4)

Combine like terms: 45x2 + 9x2 = 54x2
0 = 6(-27x + 54x2 + -15x3 + -15x3 + 5x4)

Combine like terms: -15x3 + -15x3 = -30x3
0 = 6(-27x + 54x2 + -30x3 + 5x4)
0 = (-27x * 6 + 54x2 * 6 + -30x3 * 6 + 5x4 * 6)
0 = (-162x + 324x2 + -180x3 + 30x4)

Solving
0 = -162x + 324x2 + -180x3 + 30x4

Solving for variable 'x'.
Remove the zero:
162x + -324x2 + 180x3 + -30x4 = -162x + 324x2 + -180x3 + 30x4 + 162x + -324x2 + 180x3 + -30x4

Reorder the terms:
162x + -324x2 + 180x3 + -30x4 = -162x + 162x + 324x2 + -324x2 + -180x3 + 180x3 + 30x4 + -30x4

Combine like terms: -162x + 162x = 0
162x + -324x2 + 180x3 + -30x4 = 0 + 324x2 + -324x2 + -180x3 + 180x3 + 30x4 + -30x4
162x + -324x2 + 180x3 + -30x4 = 324x2 + -324x2 + -180x3 + 180x3 + 30x4 + -30x4

Combine like terms: 324x2 + -324x2 = 0
162x + -324x2 + 180x3 + -30x4 = 0 + -180x3 + 180x3 + 30x4 + -30x4
162x + -324x2 + 180x3 + -30x4 = -180x3 + 180x3 + 30x4 + -30x4

Combine like terms: -180x3 + 180x3 = 0
162x + -324x2 + 180x3 + -30x4 = 0 + 30x4 + -30x4
162x + -324x2 + 180x3 + -30x4 = 30x4 + -30x4

Combine like terms: 30x4 + -30x4 = 0
162x + -324x2 + 180x3 + -30x4 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(27 + -54x + 30x2 + -5x3) = 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 x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(27 + -54x + 30x2 + -5x3)' equal to zero and attempt to solve:

Simplifying
27 + -54x + 30x2 + -5x3 = 0

Solving
27 + -54x + 30x2 + -5x3 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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