(x-1)(x+3)-(7x+9)(x-6)=

Solution for (x-1)(x+3)-(7x+9)(x-6)= equation:

Simplifying
(x + -1)(x + 3) + -1(7x + 9)(x + -6) = 0

Reorder the terms:
(-1 + x)(x + 3) + -1(7x + 9)(x + -6) = 0

Reorder the terms:
(-1 + x)(3 + x) + -1(7x + 9)(x + -6) = 0

Multiply (-1 + x) * (3 + x)
(-1(3 + x) + x(3 + x)) + -1(7x + 9)(x + -6) = 0
((3 * -1 + x * -1) + x(3 + x)) + -1(7x + 9)(x + -6) = 0
((-3 + -1x) + x(3 + x)) + -1(7x + 9)(x + -6) = 0
(-3 + -1x + (3 * x + x * x)) + -1(7x + 9)(x + -6) = 0
(-3 + -1x + (3x + x2)) + -1(7x + 9)(x + -6) = 0

Combine like terms: -1x + 3x = 2x
(-3 + 2x + x2) + -1(7x + 9)(x + -6) = 0

Reorder the terms:
-3 + 2x + x2 + -1(9 + 7x)(x + -6) = 0

Reorder the terms:
-3 + 2x + x2 + -1(9 + 7x)(-6 + x) = 0

Multiply (9 + 7x) * (-6 + x)
-3 + 2x + x2 + -1(9(-6 + x) + 7x * (-6 + x)) = 0
-3 + 2x + x2 + -1((-6 * 9 + x * 9) + 7x * (-6 + x)) = 0
-3 + 2x + x2 + -1((-54 + 9x) + 7x * (-6 + x)) = 0
-3 + 2x + x2 + -1(-54 + 9x + (-6 * 7x + x * 7x)) = 0
-3 + 2x + x2 + -1(-54 + 9x + (-42x + 7x2)) = 0

Combine like terms: 9x + -42x = -33x
-3 + 2x + x2 + -1(-54 + -33x + 7x2) = 0
-3 + 2x + x2 + (-54 * -1 + -33x * -1 + 7x2 * -1) = 0
-3 + 2x + x2 + (54 + 33x + -7x2) = 0

Reorder the terms:
-3 + 54 + 2x + 33x + x2 + -7x2 = 0

Combine like terms: -3 + 54 = 51
51 + 2x + 33x + x2 + -7x2 = 0

Combine like terms: 2x + 33x = 35x
51 + 35x + x2 + -7x2 = 0

Combine like terms: x2 + -7x2 = -6x2
51 + 35x + -6x2 = 0

Solving
51 + 35x + -6x2 = 0

Solving for variable 'x'.

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

Divide each side by '-6'.
-8.5 + -5.833333333x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + -5.833333333x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + -5.833333333x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + -5.833333333x + x2 = 0 + 8.5
-5.833333333x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
-5.833333333x + x2 = 8.5

The x term is -5.833333333x.  Take half its coefficient (-2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
-5.833333333x + 8.506944446 + x2 = 8.5 + 8.506944446

Reorder the terms:
8.506944446 + -5.833333333x + x2 = 8.5 + 8.506944446

Combine like terms: 8.5 + 8.506944446 = 17.006944446
8.506944446 + -5.833333333x + x2 = 17.006944446

Factor a perfect square on the left side:
(x + -2.916666667)(x + -2.916666667) = 17.006944446

Calculate the square root of the right side: 4.123947677

Break this problem into two subproblems by setting 
(x + -2.916666667) equal to 4.123947677 and -4.123947677.

Subproblem 1
x + -2.916666667 = 4.123947677

Simplifying
x + -2.916666667 = 4.123947677

Reorder the terms:
-2.916666667 + x = 4.123947677

Solving
-2.916666667 + x = 4.123947677

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = 4.123947677 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = 4.123947677 + 2.916666667
x = 4.123947677 + 2.916666667

Combine like terms: 4.123947677 + 2.916666667 = 7.040614344
x = 7.040614344

Simplifying
x = 7.040614344

Subproblem 2
x + -2.916666667 = -4.123947677

Simplifying
x + -2.916666667 = -4.123947677

Reorder the terms:
-2.916666667 + x = -4.123947677

Solving
-2.916666667 + x = -4.123947677

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.916666667' to each side of the equation.
-2.916666667 + 2.916666667 + x = -4.123947677 + 2.916666667

Combine like terms: -2.916666667 + 2.916666667 = 0.000000000
0.000000000 + x = -4.123947677 + 2.916666667
x = -4.123947677 + 2.916666667

Combine like terms: -4.123947677 + 2.916666667 = -1.20728101
x = -1.20728101

Simplifying
x = -1.20728101

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.040614344, -1.20728101}