=x+2x(x+1)+3(x+2)

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


Simplifying
0 = x + 2x(x + 1) + 3(x + 2)

Reorder the terms:
0 = x + 2x(1 + x) + 3(x + 2)
0 = x + (1 * 2x + x * 2x) + 3(x + 2)
0 = x + (2x + 2x2) + 3(x + 2)

Reorder the terms:
0 = x + 2x + 2x2 + 3(2 + x)
0 = x + 2x + 2x2 + (2 * 3 + x * 3)
0 = x + 2x + 2x2 + (6 + 3x)

Reorder the terms:
0 = 6 + x + 2x + 3x + 2x2

Combine like terms: x + 2x = 3x
0 = 6 + 3x + 3x + 2x2

Combine like terms: 3x + 3x = 6x
0 = 6 + 6x + 2x2

Solving
0 = 6 + 6x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -6x + -2x2 = 6 + 6x + 2x2 + -6 + -6x + -2x2

Reorder the terms:
-6 + -6x + -2x2 = 6 + -6 + 6x + -6x + 2x2 + -2x2

Combine like terms: 6 + -6 = 0
-6 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2
-6 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2

Combine like terms: 6x + -6x = 0
-6 + -6x + -2x2 = 0 + 2x2 + -2x2
-6 + -6x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + -6x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 3x + x2) = 0

Ignore the factor -2.

Subproblem 1
Set the factor '(3 + 3x + x2)' equal to zero and attempt to solve:

Simplifying
3 + 3x + x2 = 0

Solving
3 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 3x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 3x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 3x + x2 = 0 + -3
3x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
3x + x2 = -3

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -3 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + 3x + x2 = -0.75

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -0.75

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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