3x=(x+1)(x+3)+8

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Solution for 3x=(x+1)(x+3)+8 equation: 


Simplifying
3x = (x + 1)(x + 3) + 8

Reorder the terms:
3x = (1 + x)(x + 3) + 8

Reorder the terms:
3x = (1 + x)(3 + x) + 8

Multiply (1 + x) * (3 + x)
3x = (1(3 + x) + x(3 + x)) + 8
3x = ((3 * 1 + x * 1) + x(3 + x)) + 8
3x = ((3 + 1x) + x(3 + x)) + 8
3x = (3 + 1x + (3 * x + x * x)) + 8
3x = (3 + 1x + (3x + x2)) + 8

Combine like terms: 1x + 3x = 4x
3x = (3 + 4x + x2) + 8

Reorder the terms:
3x = 3 + 8 + 4x + x2

Combine like terms: 3 + 8 = 11
3x = 11 + 4x + x2

Solving
3x = 11 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
-11 + 3x + -4x + -1x2 = 11 + 4x + x2 + -11 + -4x + -1x2

Combine like terms: 3x + -4x = -1x
-11 + -1x + -1x2 = 11 + 4x + x2 + -11 + -4x + -1x2

Reorder the terms:
-11 + -1x + -1x2 = 11 + -11 + 4x + -4x + x2 + -1x2

Combine like terms: 11 + -11 = 0
-11 + -1x + -1x2 = 0 + 4x + -4x + x2 + -1x2
-11 + -1x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-11 + -1x + -1x2 = 0 + x2 + -1x2
-11 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(11 + x + x2)' equal to zero and attempt to solve:

Simplifying
11 + x + x2 = 0

Solving
11 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + x + x2 = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x + x2 = 0 + -11
x + x2 = 0 + -11

Combine like terms: 0 + -11 = -11
x + x2 = -11

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -11 + 0.25

Reorder the terms:
0.25 + x + x2 = -11 + 0.25

Combine like terms: -11 + 0.25 = -10.75
0.25 + x + x2 = -10.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -10.75

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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