45x=(13+x)(10+x)(4+x)

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Solution for 45x=(13+x)(10+x)(4+x) equation: 


Simplifying
45x = (13 + x)(10 + x)(4 + x)

Multiply (13 + x) * (10 + x)
45x = (13(10 + x) + x(10 + x))(4 + x)
45x = ((10 * 13 + x * 13) + x(10 + x))(4 + x)
45x = ((130 + 13x) + x(10 + x))(4 + x)
45x = (130 + 13x + (10 * x + x * x))(4 + x)
45x = (130 + 13x + (10x + x2))(4 + x)

Combine like terms: 13x + 10x = 23x
45x = (130 + 23x + x2)(4 + x)

Multiply (130 + 23x + x2) * (4 + x)
45x = (130(4 + x) + 23x * (4 + x) + x2(4 + x))
45x = ((4 * 130 + x * 130) + 23x * (4 + x) + x2(4 + x))
45x = ((520 + 130x) + 23x * (4 + x) + x2(4 + x))
45x = (520 + 130x + (4 * 23x + x * 23x) + x2(4 + x))
45x = (520 + 130x + (92x + 23x2) + x2(4 + x))
45x = (520 + 130x + 92x + 23x2 + (4 * x2 + x * x2))
45x = (520 + 130x + 92x + 23x2 + (4x2 + x3))

Combine like terms: 130x + 92x = 222x
45x = (520 + 222x + 23x2 + 4x2 + x3)

Combine like terms: 23x2 + 4x2 = 27x2
45x = (520 + 222x + 27x2 + x3)

Solving
45x = 520 + 222x + 27x2 + x3

Solving for variable 'x'.

Reorder the terms:
-520 + 45x + -222x + -27x2 + -1x3 = 520 + 222x + 27x2 + x3 + -520 + -222x + -27x2 + -1x3

Combine like terms: 45x + -222x = -177x
-520 + -177x + -27x2 + -1x3 = 520 + 222x + 27x2 + x3 + -520 + -222x + -27x2 + -1x3

Reorder the terms:
-520 + -177x + -27x2 + -1x3 = 520 + -520 + 222x + -222x + 27x2 + -27x2 + x3 + -1x3

Combine like terms: 520 + -520 = 0
-520 + -177x + -27x2 + -1x3 = 0 + 222x + -222x + 27x2 + -27x2 + x3 + -1x3
-520 + -177x + -27x2 + -1x3 = 222x + -222x + 27x2 + -27x2 + x3 + -1x3

Combine like terms: 222x + -222x = 0
-520 + -177x + -27x2 + -1x3 = 0 + 27x2 + -27x2 + x3 + -1x3
-520 + -177x + -27x2 + -1x3 = 27x2 + -27x2 + x3 + -1x3

Combine like terms: 27x2 + -27x2 = 0
-520 + -177x + -27x2 + -1x3 = 0 + x3 + -1x3
-520 + -177x + -27x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-520 + -177x + -27x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(520 + 177x + 27x2 + x3) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(520 + 177x + 27x2 + x3)' equal to zero and attempt to solve:

Simplifying
520 + 177x + 27x2 + x3 = 0

Solving
520 + 177x + 27x2 + x3 = 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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