5(5+x)(5+2x)(5+3x)=3(3+x)(3+2x)(3+3x)

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Solution for 5(5+x)(5+2x)(5+3x)=3(3+x)(3+2x)(3+3x) equation: 


Simplifying
5(5 + x)(5 + 2x)(5 + 3x) = 3(3 + x)(3 + 2x)(3 + 3x)

Multiply (5 + x) * (5 + 2x)
5(5(5 + 2x) + x(5 + 2x))(5 + 3x) = 3(3 + x)(3 + 2x)(3 + 3x)
5((5 * 5 + 2x * 5) + x(5 + 2x))(5 + 3x) = 3(3 + x)(3 + 2x)(3 + 3x)
5((25 + 10x) + x(5 + 2x))(5 + 3x) = 3(3 + x)(3 + 2x)(3 + 3x)
5(25 + 10x + (5 * x + 2x * x))(5 + 3x) = 3(3 + x)(3 + 2x)(3 + 3x)
5(25 + 10x + (5x + 2x2))(5 + 3x) = 3(3 + x)(3 + 2x)(3 + 3x)

Combine like terms: 10x + 5x = 15x
5(25 + 15x + 2x2)(5 + 3x) = 3(3 + x)(3 + 2x)(3 + 3x)

Multiply (25 + 15x + 2x2) * (5 + 3x)
5(25(5 + 3x) + 15x * (5 + 3x) + 2x2 * (5 + 3x)) = 3(3 + x)(3 + 2x)(3 + 3x)
5((5 * 25 + 3x * 25) + 15x * (5 + 3x) + 2x2 * (5 + 3x)) = 3(3 + x)(3 + 2x)(3 + 3x)
5((125 + 75x) + 15x * (5 + 3x) + 2x2 * (5 + 3x)) = 3(3 + x)(3 + 2x)(3 + 3x)
5(125 + 75x + (5 * 15x + 3x * 15x) + 2x2 * (5 + 3x)) = 3(3 + x)(3 + 2x)(3 + 3x)
5(125 + 75x + (75x + 45x2) + 2x2 * (5 + 3x)) = 3(3 + x)(3 + 2x)(3 + 3x)
5(125 + 75x + 75x + 45x2 + (5 * 2x2 + 3x * 2x2)) = 3(3 + x)(3 + 2x)(3 + 3x)
5(125 + 75x + 75x + 45x2 + (10x2 + 6x3)) = 3(3 + x)(3 + 2x)(3 + 3x)

Combine like terms: 75x + 75x = 150x
5(125 + 150x + 45x2 + 10x2 + 6x3) = 3(3 + x)(3 + 2x)(3 + 3x)

Combine like terms: 45x2 + 10x2 = 55x2
5(125 + 150x + 55x2 + 6x3) = 3(3 + x)(3 + 2x)(3 + 3x)
(125 * 5 + 150x * 5 + 55x2 * 5 + 6x3 * 5) = 3(3 + x)(3 + 2x)(3 + 3x)
(625 + 750x + 275x2 + 30x3) = 3(3 + x)(3 + 2x)(3 + 3x)

Multiply (3 + x) * (3 + 2x)
625 + 750x + 275x2 + 30x3 = 3(3(3 + 2x) + x(3 + 2x))(3 + 3x)
625 + 750x + 275x2 + 30x3 = 3((3 * 3 + 2x * 3) + x(3 + 2x))(3 + 3x)
625 + 750x + 275x2 + 30x3 = 3((9 + 6x) + x(3 + 2x))(3 + 3x)
625 + 750x + 275x2 + 30x3 = 3(9 + 6x + (3 * x + 2x * x))(3 + 3x)
625 + 750x + 275x2 + 30x3 = 3(9 + 6x + (3x + 2x2))(3 + 3x)

Combine like terms: 6x + 3x = 9x
625 + 750x + 275x2 + 30x3 = 3(9 + 9x + 2x2)(3 + 3x)

Multiply (9 + 9x + 2x2) * (3 + 3x)
625 + 750x + 275x2 + 30x3 = 3(9(3 + 3x) + 9x * (3 + 3x) + 2x2 * (3 + 3x))
625 + 750x + 275x2 + 30x3 = 3((3 * 9 + 3x * 9) + 9x * (3 + 3x) + 2x2 * (3 + 3x))
625 + 750x + 275x2 + 30x3 = 3((27 + 27x) + 9x * (3 + 3x) + 2x2 * (3 + 3x))
625 + 750x + 275x2 + 30x3 = 3(27 + 27x + (3 * 9x + 3x * 9x) + 2x2 * (3 + 3x))
625 + 750x + 275x2 + 30x3 = 3(27 + 27x + (27x + 27x2) + 2x2 * (3 + 3x))
625 + 750x + 275x2 + 30x3 = 3(27 + 27x + 27x + 27x2 + (3 * 2x2 + 3x * 2x2))
625 + 750x + 275x2 + 30x3 = 3(27 + 27x + 27x + 27x2 + (6x2 + 6x3))

Combine like terms: 27x + 27x = 54x
625 + 750x + 275x2 + 30x3 = 3(27 + 54x + 27x2 + 6x2 + 6x3)

Combine like terms: 27x2 + 6x2 = 33x2
625 + 750x + 275x2 + 30x3 = 3(27 + 54x + 33x2 + 6x3)
625 + 750x + 275x2 + 30x3 = (27 * 3 + 54x * 3 + 33x2 * 3 + 6x3 * 3)
625 + 750x + 275x2 + 30x3 = (81 + 162x + 99x2 + 18x3)

Solving
625 + 750x + 275x2 + 30x3 = 81 + 162x + 99x2 + 18x3

Solving for variable 'x'.

Reorder the terms:
625 + -81 + 750x + -162x + 275x2 + -99x2 + 30x3 + -18x3 = 81 + 162x + 99x2 + 18x3 + -81 + -162x + -99x2 + -18x3

Combine like terms: 625 + -81 = 544
544 + 750x + -162x + 275x2 + -99x2 + 30x3 + -18x3 = 81 + 162x + 99x2 + 18x3 + -81 + -162x + -99x2 + -18x3

Combine like terms: 750x + -162x = 588x
544 + 588x + 275x2 + -99x2 + 30x3 + -18x3 = 81 + 162x + 99x2 + 18x3 + -81 + -162x + -99x2 + -18x3

Combine like terms: 275x2 + -99x2 = 176x2
544 + 588x + 176x2 + 30x3 + -18x3 = 81 + 162x + 99x2 + 18x3 + -81 + -162x + -99x2 + -18x3

Combine like terms: 30x3 + -18x3 = 12x3
544 + 588x + 176x2 + 12x3 = 81 + 162x + 99x2 + 18x3 + -81 + -162x + -99x2 + -18x3

Reorder the terms:
544 + 588x + 176x2 + 12x3 = 81 + -81 + 162x + -162x + 99x2 + -99x2 + 18x3 + -18x3

Combine like terms: 81 + -81 = 0
544 + 588x + 176x2 + 12x3 = 0 + 162x + -162x + 99x2 + -99x2 + 18x3 + -18x3
544 + 588x + 176x2 + 12x3 = 162x + -162x + 99x2 + -99x2 + 18x3 + -18x3

Combine like terms: 162x + -162x = 0
544 + 588x + 176x2 + 12x3 = 0 + 99x2 + -99x2 + 18x3 + -18x3
544 + 588x + 176x2 + 12x3 = 99x2 + -99x2 + 18x3 + -18x3

Combine like terms: 99x2 + -99x2 = 0
544 + 588x + 176x2 + 12x3 = 0 + 18x3 + -18x3
544 + 588x + 176x2 + 12x3 = 18x3 + -18x3

Combine like terms: 18x3 + -18x3 = 0
544 + 588x + 176x2 + 12x3 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(136 + 147x + 44x2 + 3x3) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(136 + 147x + 44x2 + 3x3)' equal to zero and attempt to solve:

Simplifying
136 + 147x + 44x2 + 3x3 = 0

Solving
136 + 147x + 44x2 + 3x3 = 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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