(x-7x)(x-8)=(x+8)(x+9)

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Solution for (x-7x)(x-8)=(x+8)(x+9) equation: 


Simplifying
(x + -7x)(x + -8) = (x + 8)(x + 9)

Combine like terms: x + -7x = -6x
(-6x)(x + -8) = (x + 8)(x + 9)

Remove parenthesis around (-6x)
-6x(x + -8) = (x + 8)(x + 9)

Reorder the terms:
-6x(-8 + x) = (x + 8)(x + 9)
(-8 * -6x + x * -6x) = (x + 8)(x + 9)
(48x + -6x2) = (x + 8)(x + 9)

Reorder the terms:
48x + -6x2 = (8 + x)(x + 9)

Reorder the terms:
48x + -6x2 = (8 + x)(9 + x)

Multiply (8 + x) * (9 + x)
48x + -6x2 = (8(9 + x) + x(9 + x))
48x + -6x2 = ((9 * 8 + x * 8) + x(9 + x))
48x + -6x2 = ((72 + 8x) + x(9 + x))
48x + -6x2 = (72 + 8x + (9 * x + x * x))
48x + -6x2 = (72 + 8x + (9x + x2))

Combine like terms: 8x + 9x = 17x
48x + -6x2 = (72 + 17x + x2)

Solving
48x + -6x2 = 72 + 17x + x2

Solving for variable 'x'.

Reorder the terms:
-72 + 48x + -17x + -6x2 + -1x2 = 72 + 17x + x2 + -72 + -17x + -1x2

Combine like terms: 48x + -17x = 31x
-72 + 31x + -6x2 + -1x2 = 72 + 17x + x2 + -72 + -17x + -1x2

Combine like terms: -6x2 + -1x2 = -7x2
-72 + 31x + -7x2 = 72 + 17x + x2 + -72 + -17x + -1x2

Reorder the terms:
-72 + 31x + -7x2 = 72 + -72 + 17x + -17x + x2 + -1x2

Combine like terms: 72 + -72 = 0
-72 + 31x + -7x2 = 0 + 17x + -17x + x2 + -1x2
-72 + 31x + -7x2 = 17x + -17x + x2 + -1x2

Combine like terms: 17x + -17x = 0
-72 + 31x + -7x2 = 0 + x2 + -1x2
-72 + 31x + -7x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-72 + 31x + -7x2 = 0

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
10.28571429 + -4.428571429x + x2 = 0

Move the constant term to the right:

Add '-10.28571429' to each side of the equation.
10.28571429 + -4.428571429x + -10.28571429 + x2 = 0 + -10.28571429

Reorder the terms:
10.28571429 + -10.28571429 + -4.428571429x + x2 = 0 + -10.28571429

Combine like terms: 10.28571429 + -10.28571429 = 0.00000000
0.00000000 + -4.428571429x + x2 = 0 + -10.28571429
-4.428571429x + x2 = 0 + -10.28571429

Combine like terms: 0 + -10.28571429 = -10.28571429
-4.428571429x + x2 = -10.28571429

The x term is -4.428571429x.  Take half its coefficient (-2.214285715).
Square it (4.903061228) and add it to both sides.

Add '4.903061228' to each side of the equation.
-4.428571429x + 4.903061228 + x2 = -10.28571429 + 4.903061228

Reorder the terms:
4.903061228 + -4.428571429x + x2 = -10.28571429 + 4.903061228

Combine like terms: -10.28571429 + 4.903061228 = -5.382653062
4.903061228 + -4.428571429x + x2 = -5.382653062

Factor a perfect square on the left side:
(x + -2.214285715)(x + -2.214285715) = -5.382653062

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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