(3x+3)(4x+4)=8x

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Solution for (3x+3)(4x+4)=8x equation: 


Simplifying
(3x + 3)(4x + 4) = 8x

Reorder the terms:
(3 + 3x)(4x + 4) = 8x

Reorder the terms:
(3 + 3x)(4 + 4x) = 8x

Multiply (3 + 3x) * (4 + 4x)
(3(4 + 4x) + 3x * (4 + 4x)) = 8x
((4 * 3 + 4x * 3) + 3x * (4 + 4x)) = 8x
((12 + 12x) + 3x * (4 + 4x)) = 8x
(12 + 12x + (4 * 3x + 4x * 3x)) = 8x
(12 + 12x + (12x + 12x2)) = 8x

Combine like terms: 12x + 12x = 24x
(12 + 24x + 12x2) = 8x

Solving
12 + 24x + 12x2 = 8x

Solving for variable 'x'.

Reorder the terms:
12 + 24x + -8x + 12x2 = 8x + -8x

Combine like terms: 24x + -8x = 16x
12 + 16x + 12x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
12 + 16x + 12x2 = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + 4x + 3x2)' equal to zero and attempt to solve:

Simplifying
3 + 4x + 3x2 = 0

Solving
3 + 4x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
1 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 1.333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 1.333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 1.333333333x + x2 = 0 + -1
1.333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
1.333333333x + x2 = -1

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = -1 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = -1 + 0.4444444442

Combine like terms: -1 + 0.4444444442 = -0.5555555558
0.4444444442 + 1.333333333x + x2 = -0.5555555558

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = -0.5555555558

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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