7((3-6x)(7-x))=x((3-6x)(7-x)-6)

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Solution for 7((3-6x)(7-x))=x((3-6x)(7-x)-6) equation: 


Simplifying
7((3 + -6x)(7 + -1x)) = x((3 + -6x)(7 + -1x) + -6)

Multiply (3 + -6x) * (7 + -1x)
7((3(7 + -1x) + -6x * (7 + -1x))) = x((3 + -6x)(7 + -1x) + -6)
7(((7 * 3 + -1x * 3) + -6x * (7 + -1x))) = x((3 + -6x)(7 + -1x) + -6)
7(((21 + -3x) + -6x * (7 + -1x))) = x((3 + -6x)(7 + -1x) + -6)
7((21 + -3x + (7 * -6x + -1x * -6x))) = x((3 + -6x)(7 + -1x) + -6)
7((21 + -3x + (-42x + 6x2))) = x((3 + -6x)(7 + -1x) + -6)

Combine like terms: -3x + -42x = -45x
7((21 + -45x + 6x2)) = x((3 + -6x)(7 + -1x) + -6)
(21 * 7 + -45x * 7 + 6x2 * 7) = x((3 + -6x)(7 + -1x) + -6)
(147 + -315x + 42x2) = x((3 + -6x)(7 + -1x) + -6)

Multiply (3 + -6x) * (7 + -1x)
147 + -315x + 42x2 = x((3(7 + -1x) + -6x * (7 + -1x)) + -6)
147 + -315x + 42x2 = x(((7 * 3 + -1x * 3) + -6x * (7 + -1x)) + -6)
147 + -315x + 42x2 = x(((21 + -3x) + -6x * (7 + -1x)) + -6)
147 + -315x + 42x2 = x((21 + -3x + (7 * -6x + -1x * -6x)) + -6)
147 + -315x + 42x2 = x((21 + -3x + (-42x + 6x2)) + -6)

Combine like terms: -3x + -42x = -45x
147 + -315x + 42x2 = x((21 + -45x + 6x2) + -6)

Reorder the terms:
147 + -315x + 42x2 = x(21 + -6 + -45x + 6x2)

Combine like terms: 21 + -6 = 15
147 + -315x + 42x2 = x(15 + -45x + 6x2)
147 + -315x + 42x2 = (15 * x + -45x * x + 6x2 * x)
147 + -315x + 42x2 = (15x + -45x2 + 6x3)

Solving
147 + -315x + 42x2 = 15x + -45x2 + 6x3

Solving for variable 'x'.

Reorder the terms:
147 + -315x + -15x + 42x2 + 45x2 + -6x3 = 15x + -45x2 + 6x3 + -15x + 45x2 + -6x3

Combine like terms: -315x + -15x = -330x
147 + -330x + 42x2 + 45x2 + -6x3 = 15x + -45x2 + 6x3 + -15x + 45x2 + -6x3

Combine like terms: 42x2 + 45x2 = 87x2
147 + -330x + 87x2 + -6x3 = 15x + -45x2 + 6x3 + -15x + 45x2 + -6x3

Reorder the terms:
147 + -330x + 87x2 + -6x3 = 15x + -15x + -45x2 + 45x2 + 6x3 + -6x3

Combine like terms: 15x + -15x = 0
147 + -330x + 87x2 + -6x3 = 0 + -45x2 + 45x2 + 6x3 + -6x3
147 + -330x + 87x2 + -6x3 = -45x2 + 45x2 + 6x3 + -6x3

Combine like terms: -45x2 + 45x2 = 0
147 + -330x + 87x2 + -6x3 = 0 + 6x3 + -6x3
147 + -330x + 87x2 + -6x3 = 6x3 + -6x3

Combine like terms: 6x3 + -6x3 = 0
147 + -330x + 87x2 + -6x3 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(49 + -110x + 29x2 + -2x3) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(49 + -110x + 29x2 + -2x3)' equal to zero and attempt to solve:

Simplifying
49 + -110x + 29x2 + -2x3 = 0

Solving
49 + -110x + 29x2 + -2x3 = 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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