(x+3)(x^2+4x+7)=x(x^2+4x+7)

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Solution for (x+3)(x^2+4x+7)=x(x^2+4x+7) equation: 


Simplifying
(x + 3)(x2 + 4x + 7) = x(x2 + 4x + 7)

Reorder the terms:
(3 + x)(x2 + 4x + 7) = x(x2 + 4x + 7)

Reorder the terms:
(3 + x)(7 + 4x + x2) = x(x2 + 4x + 7)

Multiply (3 + x) * (7 + 4x + x2)
(3(7 + 4x + x2) + x(7 + 4x + x2)) = x(x2 + 4x + 7)
((7 * 3 + 4x * 3 + x2 * 3) + x(7 + 4x + x2)) = x(x2 + 4x + 7)
((21 + 12x + 3x2) + x(7 + 4x + x2)) = x(x2 + 4x + 7)
(21 + 12x + 3x2 + (7 * x + 4x * x + x2 * x)) = x(x2 + 4x + 7)
(21 + 12x + 3x2 + (7x + 4x2 + x3)) = x(x2 + 4x + 7)

Reorder the terms:
(21 + 12x + 7x + 3x2 + 4x2 + x3) = x(x2 + 4x + 7)

Combine like terms: 12x + 7x = 19x
(21 + 19x + 3x2 + 4x2 + x3) = x(x2 + 4x + 7)

Combine like terms: 3x2 + 4x2 = 7x2
(21 + 19x + 7x2 + x3) = x(x2 + 4x + 7)

Reorder the terms:
21 + 19x + 7x2 + x3 = x(7 + 4x + x2)
21 + 19x + 7x2 + x3 = (7 * x + 4x * x + x2 * x)
21 + 19x + 7x2 + x3 = (7x + 4x2 + x3)

Add '-1x3' to each side of the equation.
21 + 19x + 7x2 + x3 + -1x3 = 7x + 4x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
21 + 19x + 7x2 + 0 = 7x + 4x2 + x3 + -1x3
21 + 19x + 7x2 = 7x + 4x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
21 + 19x + 7x2 = 7x + 4x2 + 0
21 + 19x + 7x2 = 7x + 4x2

Solving
21 + 19x + 7x2 = 7x + 4x2

Solving for variable 'x'.

Reorder the terms:
21 + 19x + -7x + 7x2 + -4x2 = 7x + 4x2 + -7x + -4x2

Combine like terms: 19x + -7x = 12x
21 + 12x + 7x2 + -4x2 = 7x + 4x2 + -7x + -4x2

Combine like terms: 7x2 + -4x2 = 3x2
21 + 12x + 3x2 = 7x + 4x2 + -7x + -4x2

Reorder the terms:
21 + 12x + 3x2 = 7x + -7x + 4x2 + -4x2

Combine like terms: 7x + -7x = 0
21 + 12x + 3x2 = 0 + 4x2 + -4x2
21 + 12x + 3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
21 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
7 + 4x + x2 = 0

Solving
7 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 4x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 4x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4x + x2 = 0 + -7
4x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
4x + x2 = -7

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -7 + 4

Reorder the terms:
4 + 4x + x2 = -7 + 4

Combine like terms: -7 + 4 = -3
4 + 4x + x2 = -3

Factor a perfect square on the left side:
(x + 2)(x + 2) = -3

Can't calculate square root of the right side.

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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