(x^2+3x+2)(x^2+7x+12)=24

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Solution for (x^2+3x+2)(x^2+7x+12)=24 equation: 


Simplifying
(x2 + 3x + 2)(x2 + 7x + 12) = 24

Reorder the terms:
(2 + 3x + x2)(x2 + 7x + 12) = 24

Reorder the terms:
(2 + 3x + x2)(12 + 7x + x2) = 24

Multiply (2 + 3x + x2) * (12 + 7x + x2)
(2(12 + 7x + x2) + 3x * (12 + 7x + x2) + x2(12 + 7x + x2)) = 24
((12 * 2 + 7x * 2 + x2 * 2) + 3x * (12 + 7x + x2) + x2(12 + 7x + x2)) = 24
((24 + 14x + 2x2) + 3x * (12 + 7x + x2) + x2(12 + 7x + x2)) = 24
(24 + 14x + 2x2 + (12 * 3x + 7x * 3x + x2 * 3x) + x2(12 + 7x + x2)) = 24
(24 + 14x + 2x2 + (36x + 21x2 + 3x3) + x2(12 + 7x + x2)) = 24
(24 + 14x + 2x2 + 36x + 21x2 + 3x3 + (12 * x2 + 7x * x2 + x2 * x2)) = 24
(24 + 14x + 2x2 + 36x + 21x2 + 3x3 + (12x2 + 7x3 + x4)) = 24

Reorder the terms:
(24 + 14x + 36x + 2x2 + 21x2 + 12x2 + 3x3 + 7x3 + x4) = 24

Combine like terms: 14x + 36x = 50x
(24 + 50x + 2x2 + 21x2 + 12x2 + 3x3 + 7x3 + x4) = 24

Combine like terms: 2x2 + 21x2 = 23x2
(24 + 50x + 23x2 + 12x2 + 3x3 + 7x3 + x4) = 24

Combine like terms: 23x2 + 12x2 = 35x2
(24 + 50x + 35x2 + 3x3 + 7x3 + x4) = 24

Combine like terms: 3x3 + 7x3 = 10x3
(24 + 50x + 35x2 + 10x3 + x4) = 24

Add '-24' to each side of the equation.
24 + 50x + 35x2 + 10x3 + -24 + x4 = 24 + -24

Reorder the terms:
24 + -24 + 50x + 35x2 + 10x3 + x4 = 24 + -24

Combine like terms: 24 + -24 = 0
0 + 50x + 35x2 + 10x3 + x4 = 24 + -24
50x + 35x2 + 10x3 + x4 = 24 + -24

Combine like terms: 24 + -24 = 0
50x + 35x2 + 10x3 + x4 = 0

Solving
50x + 35x2 + 10x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(50 + 35x + 10x2 + 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 '(50 + 35x + 10x2 + x3)' equal to zero and attempt to solve:

Simplifying
50 + 35x + 10x2 + x3 = 0

Solving
50 + 35x + 10x2 + 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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