x(x+7)=2(x+7)(x-3)+168

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Solution for x(x+7)=2(x+7)(x-3)+168 equation: 


Simplifying
x(x + 7) = 2(x + 7)(x + -3) + 168

Reorder the terms:
x(7 + x) = 2(x + 7)(x + -3) + 168
(7 * x + x * x) = 2(x + 7)(x + -3) + 168
(7x + x2) = 2(x + 7)(x + -3) + 168

Reorder the terms:
7x + x2 = 2(7 + x)(x + -3) + 168

Reorder the terms:
7x + x2 = 2(7 + x)(-3 + x) + 168

Multiply (7 + x) * (-3 + x)
7x + x2 = 2(7(-3 + x) + x(-3 + x)) + 168
7x + x2 = 2((-3 * 7 + x * 7) + x(-3 + x)) + 168
7x + x2 = 2((-21 + 7x) + x(-3 + x)) + 168
7x + x2 = 2(-21 + 7x + (-3 * x + x * x)) + 168
7x + x2 = 2(-21 + 7x + (-3x + x2)) + 168

Combine like terms: 7x + -3x = 4x
7x + x2 = 2(-21 + 4x + x2) + 168
7x + x2 = (-21 * 2 + 4x * 2 + x2 * 2) + 168
7x + x2 = (-42 + 8x + 2x2) + 168

Reorder the terms:
7x + x2 = -42 + 168 + 8x + 2x2

Combine like terms: -42 + 168 = 126
7x + x2 = 126 + 8x + 2x2

Solving
7x + x2 = 126 + 8x + 2x2

Solving for variable 'x'.

Reorder the terms:
-126 + 7x + -8x + x2 + -2x2 = 126 + 8x + 2x2 + -126 + -8x + -2x2

Combine like terms: 7x + -8x = -1x
-126 + -1x + x2 + -2x2 = 126 + 8x + 2x2 + -126 + -8x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-126 + -1x + -1x2 = 126 + 8x + 2x2 + -126 + -8x + -2x2

Reorder the terms:
-126 + -1x + -1x2 = 126 + -126 + 8x + -8x + 2x2 + -2x2

Combine like terms: 126 + -126 = 0
-126 + -1x + -1x2 = 0 + 8x + -8x + 2x2 + -2x2
-126 + -1x + -1x2 = 8x + -8x + 2x2 + -2x2

Combine like terms: 8x + -8x = 0
-126 + -1x + -1x2 = 0 + 2x2 + -2x2
-126 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-126 + -1x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(126 + x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(126 + x + x2)' equal to zero and attempt to solve:

Simplifying
126 + x + x2 = 0

Solving
126 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-126' to each side of the equation.
126 + x + -126 + x2 = 0 + -126

Reorder the terms:
126 + -126 + x + x2 = 0 + -126

Combine like terms: 126 + -126 = 0
0 + x + x2 = 0 + -126
x + x2 = 0 + -126

Combine like terms: 0 + -126 = -126
x + x2 = -126

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 = -126 + 0.25

Reorder the terms:
0.25 + x + x2 = -126 + 0.25

Combine like terms: -126 + 0.25 = -125.75
0.25 + x + x2 = -125.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -125.75

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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