6x^3+18x^2-240=6x(x-a)(x-b)

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Solution for 6x^3+18x^2-240=6x(x-a)(x-b) equation: 


Simplifying
6x3 + 18x2 + -240 = 6x(x + -1a)(x + -1b)

Reorder the terms:
-240 + 18x2 + 6x3 = 6x(x + -1a)(x + -1b)

Reorder the terms:
-240 + 18x2 + 6x3 = 6x(-1a + x)(x + -1b)

Reorder the terms:
-240 + 18x2 + 6x3 = 6x(-1a + x)(-1b + x)

Multiply (-1a + x) * (-1b + x)
-240 + 18x2 + 6x3 = 6x(-1a * (-1b + x) + x(-1b + x))
-240 + 18x2 + 6x3 = 6x((-1b * -1a + x * -1a) + x(-1b + x))
-240 + 18x2 + 6x3 = 6x((1ab + -1ax) + x(-1b + x))
-240 + 18x2 + 6x3 = 6x(1ab + -1ax + (-1b * x + x * x))
-240 + 18x2 + 6x3 = 6x(1ab + -1ax + (-1bx + x2))
-240 + 18x2 + 6x3 = 6x(1ab + -1ax + -1bx + x2)
-240 + 18x2 + 6x3 = (1ab * 6x + -1ax * 6x + -1bx * 6x + x2 * 6x)
-240 + 18x2 + 6x3 = (6abx + -6ax2 + -6bx2 + 6x3)

Add '-6x3' to each side of the equation.
-240 + 18x2 + 6x3 + -6x3 = 6abx + -6ax2 + -6bx2 + 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
-240 + 18x2 + 0 = 6abx + -6ax2 + -6bx2 + 6x3 + -6x3
-240 + 18x2 = 6abx + -6ax2 + -6bx2 + 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
-240 + 18x2 = 6abx + -6ax2 + -6bx2 + 0
-240 + 18x2 = 6abx + -6ax2 + -6bx2

Solving
-240 + 18x2 = 6abx + -6ax2 + -6bx2

Solving for variable 'x'.

Reorder the terms:
-240 + -6abx + 6ax2 + 6bx2 + 18x2 = 6abx + -6ax2 + -6bx2 + -6abx + 6ax2 + 6bx2

Reorder the terms:
-240 + -6abx + 6ax2 + 6bx2 + 18x2 = 6abx + -6abx + -6ax2 + 6ax2 + -6bx2 + 6bx2

Combine like terms: 6abx + -6abx = 0
-240 + -6abx + 6ax2 + 6bx2 + 18x2 = 0 + -6ax2 + 6ax2 + -6bx2 + 6bx2
-240 + -6abx + 6ax2 + 6bx2 + 18x2 = -6ax2 + 6ax2 + -6bx2 + 6bx2

Combine like terms: -6ax2 + 6ax2 = 0
-240 + -6abx + 6ax2 + 6bx2 + 18x2 = 0 + -6bx2 + 6bx2
-240 + -6abx + 6ax2 + 6bx2 + 18x2 = -6bx2 + 6bx2

Combine like terms: -6bx2 + 6bx2 = 0
-240 + -6abx + 6ax2 + 6bx2 + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-40 + -1abx + ax2 + bx2 + 3x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-40 + -1abx + ax2 + bx2 + 3x2)' equal to zero and attempt to solve:

Simplifying
-40 + -1abx + ax2 + bx2 + 3x2 = 0

Solving
-40 + -1abx + ax2 + bx2 + 3x2 = 0

The solution to this equation could not be determined.

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

The solution to this equation could not be determined.

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