(2x+3)(x^2+1)=(-3x-7)(x^2+1)

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Solution for (2x+3)(x^2+1)=(-3x-7)(x^2+1) equation: 


Simplifying
(2x + 3)(x2 + 1) = (-3x + -7)(x2 + 1)

Reorder the terms:
(3 + 2x)(x2 + 1) = (-3x + -7)(x2 + 1)

Reorder the terms:
(3 + 2x)(1 + x2) = (-3x + -7)(x2 + 1)

Multiply (3 + 2x) * (1 + x2)
(3(1 + x2) + 2x * (1 + x2)) = (-3x + -7)(x2 + 1)
((1 * 3 + x2 * 3) + 2x * (1 + x2)) = (-3x + -7)(x2 + 1)
((3 + 3x2) + 2x * (1 + x2)) = (-3x + -7)(x2 + 1)
(3 + 3x2 + (1 * 2x + x2 * 2x)) = (-3x + -7)(x2 + 1)
(3 + 3x2 + (2x + 2x3)) = (-3x + -7)(x2 + 1)

Reorder the terms:
(3 + 2x + 3x2 + 2x3) = (-3x + -7)(x2 + 1)
(3 + 2x + 3x2 + 2x3) = (-3x + -7)(x2 + 1)

Reorder the terms:
3 + 2x + 3x2 + 2x3 = (-7 + -3x)(x2 + 1)

Reorder the terms:
3 + 2x + 3x2 + 2x3 = (-7 + -3x)(1 + x2)

Multiply (-7 + -3x) * (1 + x2)
3 + 2x + 3x2 + 2x3 = (-7(1 + x2) + -3x * (1 + x2))
3 + 2x + 3x2 + 2x3 = ((1 * -7 + x2 * -7) + -3x * (1 + x2))
3 + 2x + 3x2 + 2x3 = ((-7 + -7x2) + -3x * (1 + x2))
3 + 2x + 3x2 + 2x3 = (-7 + -7x2 + (1 * -3x + x2 * -3x))
3 + 2x + 3x2 + 2x3 = (-7 + -7x2 + (-3x + -3x3))

Reorder the terms:
3 + 2x + 3x2 + 2x3 = (-7 + -3x + -7x2 + -3x3)
3 + 2x + 3x2 + 2x3 = (-7 + -3x + -7x2 + -3x3)

Solving
3 + 2x + 3x2 + 2x3 = -7 + -3x + -7x2 + -3x3

Solving for variable 'x'.

Reorder the terms:
3 + 7 + 2x + 3x + 3x2 + 7x2 + 2x3 + 3x3 = -7 + -3x + -7x2 + -3x3 + 7 + 3x + 7x2 + 3x3

Combine like terms: 3 + 7 = 10
10 + 2x + 3x + 3x2 + 7x2 + 2x3 + 3x3 = -7 + -3x + -7x2 + -3x3 + 7 + 3x + 7x2 + 3x3

Combine like terms: 2x + 3x = 5x
10 + 5x + 3x2 + 7x2 + 2x3 + 3x3 = -7 + -3x + -7x2 + -3x3 + 7 + 3x + 7x2 + 3x3

Combine like terms: 3x2 + 7x2 = 10x2
10 + 5x + 10x2 + 2x3 + 3x3 = -7 + -3x + -7x2 + -3x3 + 7 + 3x + 7x2 + 3x3

Combine like terms: 2x3 + 3x3 = 5x3
10 + 5x + 10x2 + 5x3 = -7 + -3x + -7x2 + -3x3 + 7 + 3x + 7x2 + 3x3

Reorder the terms:
10 + 5x + 10x2 + 5x3 = -7 + 7 + -3x + 3x + -7x2 + 7x2 + -3x3 + 3x3

Combine like terms: -7 + 7 = 0
10 + 5x + 10x2 + 5x3 = 0 + -3x + 3x + -7x2 + 7x2 + -3x3 + 3x3
10 + 5x + 10x2 + 5x3 = -3x + 3x + -7x2 + 7x2 + -3x3 + 3x3

Combine like terms: -3x + 3x = 0
10 + 5x + 10x2 + 5x3 = 0 + -7x2 + 7x2 + -3x3 + 3x3
10 + 5x + 10x2 + 5x3 = -7x2 + 7x2 + -3x3 + 3x3

Combine like terms: -7x2 + 7x2 = 0
10 + 5x + 10x2 + 5x3 = 0 + -3x3 + 3x3
10 + 5x + 10x2 + 5x3 = -3x3 + 3x3

Combine like terms: -3x3 + 3x3 = 0
10 + 5x + 10x2 + 5x3 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + x + 2x2 + x3) = 0

Ignore the factor 5.

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

Simplifying
2 + x + 2x2 + x3 = 0

Solving
2 + x + 2x2 + 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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