3(x-7)=(3x+2)(2x+1)

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Solution for 3(x-7)=(3x+2)(2x+1) equation: 


Simplifying
3(x + -7) = (3x + 2)(2x + 1)

Reorder the terms:
3(-7 + x) = (3x + 2)(2x + 1)
(-7 * 3 + x * 3) = (3x + 2)(2x + 1)
(-21 + 3x) = (3x + 2)(2x + 1)

Reorder the terms:
-21 + 3x = (2 + 3x)(2x + 1)

Reorder the terms:
-21 + 3x = (2 + 3x)(1 + 2x)

Multiply (2 + 3x) * (1 + 2x)
-21 + 3x = (2(1 + 2x) + 3x * (1 + 2x))
-21 + 3x = ((1 * 2 + 2x * 2) + 3x * (1 + 2x))
-21 + 3x = ((2 + 4x) + 3x * (1 + 2x))
-21 + 3x = (2 + 4x + (1 * 3x + 2x * 3x))
-21 + 3x = (2 + 4x + (3x + 6x2))

Combine like terms: 4x + 3x = 7x
-21 + 3x = (2 + 7x + 6x2)

Solving
-21 + 3x = 2 + 7x + 6x2

Solving for variable 'x'.

Reorder the terms:
-21 + -2 + 3x + -7x + -6x2 = 2 + 7x + 6x2 + -2 + -7x + -6x2

Combine like terms: -21 + -2 = -23
-23 + 3x + -7x + -6x2 = 2 + 7x + 6x2 + -2 + -7x + -6x2

Combine like terms: 3x + -7x = -4x
-23 + -4x + -6x2 = 2 + 7x + 6x2 + -2 + -7x + -6x2

Reorder the terms:
-23 + -4x + -6x2 = 2 + -2 + 7x + -7x + 6x2 + -6x2

Combine like terms: 2 + -2 = 0
-23 + -4x + -6x2 = 0 + 7x + -7x + 6x2 + -6x2
-23 + -4x + -6x2 = 7x + -7x + 6x2 + -6x2

Combine like terms: 7x + -7x = 0
-23 + -4x + -6x2 = 0 + 6x2 + -6x2
-23 + -4x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-23 + -4x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(23 + 4x + 6x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(23 + 4x + 6x2)' equal to zero and attempt to solve:

Simplifying
23 + 4x + 6x2 = 0

Solving
23 + 4x + 6x2 = 0

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

Divide each side by '6'.
3.833333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-3.833333333' to each side of the equation.
3.833333333 + 0.6666666667x + -3.833333333 + x2 = 0 + -3.833333333

Reorder the terms:
3.833333333 + -3.833333333 + 0.6666666667x + x2 = 0 + -3.833333333

Combine like terms: 3.833333333 + -3.833333333 = 0.000000000
0.000000000 + 0.6666666667x + x2 = 0 + -3.833333333
0.6666666667x + x2 = 0 + -3.833333333

Combine like terms: 0 + -3.833333333 = -3.833333333
0.6666666667x + x2 = -3.833333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = -3.833333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = -3.833333333 + 0.1111111112

Combine like terms: -3.833333333 + 0.1111111112 = -3.7222222218
0.1111111112 + 0.6666666667x + x2 = -3.7222222218

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = -3.7222222218

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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