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

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Solution for 14(x-4)-(x+2)=(x+2)(x+4) equation:


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

Reorder the terms:
14(-4 + x) + -1(x + 2) = (x + 2)(x + 4)
(-4 * 14 + x * 14) + -1(x + 2) = (x + 2)(x + 4)
(-56 + 14x) + -1(x + 2) = (x + 2)(x + 4)

Reorder the terms:
-56 + 14x + -1(2 + x) = (x + 2)(x + 4)
-56 + 14x + (2 * -1 + x * -1) = (x + 2)(x + 4)
-56 + 14x + (-2 + -1x) = (x + 2)(x + 4)

Reorder the terms:
-56 + -2 + 14x + -1x = (x + 2)(x + 4)

Combine like terms: -56 + -2 = -58
-58 + 14x + -1x = (x + 2)(x + 4)

Combine like terms: 14x + -1x = 13x
-58 + 13x = (x + 2)(x + 4)

Reorder the terms:
-58 + 13x = (2 + x)(x + 4)

Reorder the terms:
-58 + 13x = (2 + x)(4 + x)

Multiply (2 + x) * (4 + x)
-58 + 13x = (2(4 + x) + x(4 + x))
-58 + 13x = ((4 * 2 + x * 2) + x(4 + x))
-58 + 13x = ((8 + 2x) + x(4 + x))
-58 + 13x = (8 + 2x + (4 * x + x * x))
-58 + 13x = (8 + 2x + (4x + x2))

Combine like terms: 2x + 4x = 6x
-58 + 13x = (8 + 6x + x2)

Solving
-58 + 13x = 8 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-58 + -8 + 13x + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: -58 + -8 = -66
-66 + 13x + -6x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Combine like terms: 13x + -6x = 7x
-66 + 7x + -1x2 = 8 + 6x + x2 + -8 + -6x + -1x2

Reorder the terms:
-66 + 7x + -1x2 = 8 + -8 + 6x + -6x + x2 + -1x2

Combine like terms: 8 + -8 = 0
-66 + 7x + -1x2 = 0 + 6x + -6x + x2 + -1x2
-66 + 7x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
-66 + 7x + -1x2 = 0 + x2 + -1x2
-66 + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-66 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
66 + -7x + x2 = 0

Move the constant term to the right:

Add '-66' to each side of the equation.
66 + -7x + -66 + x2 = 0 + -66

Reorder the terms:
66 + -66 + -7x + x2 = 0 + -66

Combine like terms: 66 + -66 = 0
0 + -7x + x2 = 0 + -66
-7x + x2 = 0 + -66

Combine like terms: 0 + -66 = -66
-7x + x2 = -66

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -66 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -66 + 12.25

Combine like terms: -66 + 12.25 = -53.75
12.25 + -7x + x2 = -53.75

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = -53.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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