(5x-6)(x-9)=(x+1)(1-6x)

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Solution for (5x-6)(x-9)=(x+1)(1-6x) equation: 


Simplifying
(5x + -6)(x + -9) = (x + 1)(1 + -6x)

Reorder the terms:
(-6 + 5x)(x + -9) = (x + 1)(1 + -6x)

Reorder the terms:
(-6 + 5x)(-9 + x) = (x + 1)(1 + -6x)

Multiply (-6 + 5x) * (-9 + x)
(-6(-9 + x) + 5x * (-9 + x)) = (x + 1)(1 + -6x)
((-9 * -6 + x * -6) + 5x * (-9 + x)) = (x + 1)(1 + -6x)
((54 + -6x) + 5x * (-9 + x)) = (x + 1)(1 + -6x)
(54 + -6x + (-9 * 5x + x * 5x)) = (x + 1)(1 + -6x)
(54 + -6x + (-45x + 5x2)) = (x + 1)(1 + -6x)

Combine like terms: -6x + -45x = -51x
(54 + -51x + 5x2) = (x + 1)(1 + -6x)

Reorder the terms:
54 + -51x + 5x2 = (1 + x)(1 + -6x)

Multiply (1 + x) * (1 + -6x)
54 + -51x + 5x2 = (1(1 + -6x) + x(1 + -6x))
54 + -51x + 5x2 = ((1 * 1 + -6x * 1) + x(1 + -6x))
54 + -51x + 5x2 = ((1 + -6x) + x(1 + -6x))
54 + -51x + 5x2 = (1 + -6x + (1 * x + -6x * x))
54 + -51x + 5x2 = (1 + -6x + (1x + -6x2))

Combine like terms: -6x + 1x = -5x
54 + -51x + 5x2 = (1 + -5x + -6x2)

Solving
54 + -51x + 5x2 = 1 + -5x + -6x2

Solving for variable 'x'.

Reorder the terms:
54 + -1 + -51x + 5x + 5x2 + 6x2 = 1 + -5x + -6x2 + -1 + 5x + 6x2

Combine like terms: 54 + -1 = 53
53 + -51x + 5x + 5x2 + 6x2 = 1 + -5x + -6x2 + -1 + 5x + 6x2

Combine like terms: -51x + 5x = -46x
53 + -46x + 5x2 + 6x2 = 1 + -5x + -6x2 + -1 + 5x + 6x2

Combine like terms: 5x2 + 6x2 = 11x2
53 + -46x + 11x2 = 1 + -5x + -6x2 + -1 + 5x + 6x2

Reorder the terms:
53 + -46x + 11x2 = 1 + -1 + -5x + 5x + -6x2 + 6x2

Combine like terms: 1 + -1 = 0
53 + -46x + 11x2 = 0 + -5x + 5x + -6x2 + 6x2
53 + -46x + 11x2 = -5x + 5x + -6x2 + 6x2

Combine like terms: -5x + 5x = 0
53 + -46x + 11x2 = 0 + -6x2 + 6x2
53 + -46x + 11x2 = -6x2 + 6x2

Combine like terms: -6x2 + 6x2 = 0
53 + -46x + 11x2 = 0

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

Divide each side by '11'.
4.818181818 + -4.181818182x + x2 = 0

Move the constant term to the right:

Add '-4.818181818' to each side of the equation.
4.818181818 + -4.181818182x + -4.818181818 + x2 = 0 + -4.818181818

Reorder the terms:
4.818181818 + -4.818181818 + -4.181818182x + x2 = 0 + -4.818181818

Combine like terms: 4.818181818 + -4.818181818 = 0.000000000
0.000000000 + -4.181818182x + x2 = 0 + -4.818181818
-4.181818182x + x2 = 0 + -4.818181818

Combine like terms: 0 + -4.818181818 = -4.818181818
-4.181818182x + x2 = -4.818181818

The x term is -4.181818182x.  Take half its coefficient (-2.090909091).
Square it (4.371900827) and add it to both sides.

Add '4.371900827' to each side of the equation.
-4.181818182x + 4.371900827 + x2 = -4.818181818 + 4.371900827

Reorder the terms:
4.371900827 + -4.181818182x + x2 = -4.818181818 + 4.371900827

Combine like terms: -4.818181818 + 4.371900827 = -0.446280991
4.371900827 + -4.181818182x + x2 = -0.446280991

Factor a perfect square on the left side:
(x + -2.090909091)(x + -2.090909091) = -0.446280991

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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