(x+1)(x+2)(x+4)(x+5)=40

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Solution for (x+1)(x+2)(x+4)(x+5)=40 equation: 


Simplifying
(x + 1)(x + 2)(x + 4)(x + 5) = 40

Reorder the terms:
(1 + x)(x + 2)(x + 4)(x + 5) = 40

Reorder the terms:
(1 + x)(2 + x)(x + 4)(x + 5) = 40

Reorder the terms:
(1 + x)(2 + x)(4 + x)(x + 5) = 40

Reorder the terms:
(1 + x)(2 + x)(4 + x)(5 + x) = 40

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x))(4 + x)(5 + x) = 40
((2 * 1 + x * 1) + x(2 + x))(4 + x)(5 + x) = 40
((2 + 1x) + x(2 + x))(4 + x)(5 + x) = 40
(2 + 1x + (2 * x + x * x))(4 + x)(5 + x) = 40
(2 + 1x + (2x + x2))(4 + x)(5 + x) = 40

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2)(4 + x)(5 + x) = 40

Multiply (2 + 3x + x2) * (4 + x)
(2(4 + x) + 3x * (4 + x) + x2(4 + x))(5 + x) = 40
((4 * 2 + x * 2) + 3x * (4 + x) + x2(4 + x))(5 + x) = 40
((8 + 2x) + 3x * (4 + x) + x2(4 + x))(5 + x) = 40
(8 + 2x + (4 * 3x + x * 3x) + x2(4 + x))(5 + x) = 40
(8 + 2x + (12x + 3x2) + x2(4 + x))(5 + x) = 40
(8 + 2x + 12x + 3x2 + (4 * x2 + x * x2))(5 + x) = 40
(8 + 2x + 12x + 3x2 + (4x2 + x3))(5 + x) = 40

Combine like terms: 2x + 12x = 14x
(8 + 14x + 3x2 + 4x2 + x3)(5 + x) = 40

Combine like terms: 3x2 + 4x2 = 7x2
(8 + 14x + 7x2 + x3)(5 + x) = 40

Multiply (8 + 14x + 7x2 + x3) * (5 + x)
(8(5 + x) + 14x * (5 + x) + 7x2 * (5 + x) + x3(5 + x)) = 40
((5 * 8 + x * 8) + 14x * (5 + x) + 7x2 * (5 + x) + x3(5 + x)) = 40
((40 + 8x) + 14x * (5 + x) + 7x2 * (5 + x) + x3(5 + x)) = 40
(40 + 8x + (5 * 14x + x * 14x) + 7x2 * (5 + x) + x3(5 + x)) = 40
(40 + 8x + (70x + 14x2) + 7x2 * (5 + x) + x3(5 + x)) = 40
(40 + 8x + 70x + 14x2 + (5 * 7x2 + x * 7x2) + x3(5 + x)) = 40
(40 + 8x + 70x + 14x2 + (35x2 + 7x3) + x3(5 + x)) = 40
(40 + 8x + 70x + 14x2 + 35x2 + 7x3 + (5 * x3 + x * x3)) = 40
(40 + 8x + 70x + 14x2 + 35x2 + 7x3 + (5x3 + x4)) = 40

Combine like terms: 8x + 70x = 78x
(40 + 78x + 14x2 + 35x2 + 7x3 + 5x3 + x4) = 40

Combine like terms: 14x2 + 35x2 = 49x2
(40 + 78x + 49x2 + 7x3 + 5x3 + x4) = 40

Combine like terms: 7x3 + 5x3 = 12x3
(40 + 78x + 49x2 + 12x3 + x4) = 40

Add '-40' to each side of the equation.
40 + 78x + 49x2 + 12x3 + -40 + x4 = 40 + -40

Reorder the terms:
40 + -40 + 78x + 49x2 + 12x3 + x4 = 40 + -40

Combine like terms: 40 + -40 = 0
0 + 78x + 49x2 + 12x3 + x4 = 40 + -40
78x + 49x2 + 12x3 + x4 = 40 + -40

Combine like terms: 40 + -40 = 0
78x + 49x2 + 12x3 + x4 = 0

Solving
78x + 49x2 + 12x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(78 + 49x + 12x2 + x3) = 0


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 '(78 + 49x + 12x2 + x3)' equal to zero and attempt to solve:

Simplifying
78 + 49x + 12x2 + x3 = 0

Solving
78 + 49x + 12x2 + x3 = 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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