2(x+1)(x+2)=4(x-1)

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Solution for 2(x+1)(x+2)=4(x-1) equation: 


Simplifying
2(x + 1)(x + 2) = 4(x + -1)

Reorder the terms:
2(1 + x)(x + 2) = 4(x + -1)

Reorder the terms:
2(1 + x)(2 + x) = 4(x + -1)

Multiply (1 + x) * (2 + x)
2(1(2 + x) + x(2 + x)) = 4(x + -1)
2((2 * 1 + x * 1) + x(2 + x)) = 4(x + -1)
2((2 + 1x) + x(2 + x)) = 4(x + -1)
2(2 + 1x + (2 * x + x * x)) = 4(x + -1)
2(2 + 1x + (2x + x2)) = 4(x + -1)

Combine like terms: 1x + 2x = 3x
2(2 + 3x + x2) = 4(x + -1)
(2 * 2 + 3x * 2 + x2 * 2) = 4(x + -1)
(4 + 6x + 2x2) = 4(x + -1)

Reorder the terms:
4 + 6x + 2x2 = 4(-1 + x)
4 + 6x + 2x2 = (-1 * 4 + x * 4)
4 + 6x + 2x2 = (-4 + 4x)

Solving
4 + 6x + 2x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:
4 + 4 + 6x + -4x + 2x2 = -4 + 4x + 4 + -4x

Combine like terms: 4 + 4 = 8
8 + 6x + -4x + 2x2 = -4 + 4x + 4 + -4x

Combine like terms: 6x + -4x = 2x
8 + 2x + 2x2 = -4 + 4x + 4 + -4x

Reorder the terms:
8 + 2x + 2x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
8 + 2x + 2x2 = 0 + 4x + -4x
8 + 2x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
8 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + x + x2) = 0

Ignore the factor 2.

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

Simplifying
4 + x + x2 = 0

Solving
4 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = -4 + 0.25

Reorder the terms:
0.25 + x + x2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + x + x2 = -3.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -3.75

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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