(x-3)(x+5)-(-5x-2)(x-1)=

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Solution for (x-3)(x+5)-(-5x-2)(x-1)= equation: 


Simplifying
(x + -3)(x + 5) + -1(-5x + -2)(x + -1) = 0

Reorder the terms:
(-3 + x)(x + 5) + -1(-5x + -2)(x + -1) = 0

Reorder the terms:
(-3 + x)(5 + x) + -1(-5x + -2)(x + -1) = 0

Multiply (-3 + x) * (5 + x)
(-3(5 + x) + x(5 + x)) + -1(-5x + -2)(x + -1) = 0
((5 * -3 + x * -3) + x(5 + x)) + -1(-5x + -2)(x + -1) = 0
((-15 + -3x) + x(5 + x)) + -1(-5x + -2)(x + -1) = 0
(-15 + -3x + (5 * x + x * x)) + -1(-5x + -2)(x + -1) = 0
(-15 + -3x + (5x + x2)) + -1(-5x + -2)(x + -1) = 0

Combine like terms: -3x + 5x = 2x
(-15 + 2x + x2) + -1(-5x + -2)(x + -1) = 0

Reorder the terms:
-15 + 2x + x2 + -1(-2 + -5x)(x + -1) = 0

Reorder the terms:
-15 + 2x + x2 + -1(-2 + -5x)(-1 + x) = 0

Multiply (-2 + -5x) * (-1 + x)
-15 + 2x + x2 + -1(-2(-1 + x) + -5x * (-1 + x)) = 0
-15 + 2x + x2 + -1((-1 * -2 + x * -2) + -5x * (-1 + x)) = 0
-15 + 2x + x2 + -1((2 + -2x) + -5x * (-1 + x)) = 0
-15 + 2x + x2 + -1(2 + -2x + (-1 * -5x + x * -5x)) = 0
-15 + 2x + x2 + -1(2 + -2x + (5x + -5x2)) = 0

Combine like terms: -2x + 5x = 3x
-15 + 2x + x2 + -1(2 + 3x + -5x2) = 0
-15 + 2x + x2 + (2 * -1 + 3x * -1 + -5x2 * -1) = 0
-15 + 2x + x2 + (-2 + -3x + 5x2) = 0

Reorder the terms:
-15 + -2 + 2x + -3x + x2 + 5x2 = 0

Combine like terms: -15 + -2 = -17
-17 + 2x + -3x + x2 + 5x2 = 0

Combine like terms: 2x + -3x = -1x
-17 + -1x + x2 + 5x2 = 0

Combine like terms: x2 + 5x2 = 6x2
-17 + -1x + 6x2 = 0

Solving
-17 + -1x + 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'.
-2.833333333 + -0.1666666667x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + -0.1666666667x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + -0.1666666667x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + -0.1666666667x + x2 = 0 + 2.833333333
-0.1666666667x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
-0.1666666667x + x2 = 2.833333333

The x term is -0.1666666667x.  Take half its coefficient (-0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
-0.1666666667x + 0.006944444447 + x2 = 2.833333333 + 0.006944444447

Reorder the terms:
0.006944444447 + -0.1666666667x + x2 = 2.833333333 + 0.006944444447

Combine like terms: 2.833333333 + 0.006944444447 = 2.840277777447
0.006944444447 + -0.1666666667x + x2 = 2.840277777447

Factor a perfect square on the left side:
(x + -0.08333333335)(x + -0.08333333335) = 2.840277777447

Calculate the square root of the right side: 1.685312368

Break this problem into two subproblems by setting 
(x + -0.08333333335) equal to 1.685312368 and -1.685312368.


Subproblem 1
x + -0.08333333335 = 1.685312368

Simplifying
x + -0.08333333335 = 1.685312368

Reorder the terms:
-0.08333333335 + x = 1.685312368

Solving
-0.08333333335 + x = 1.685312368

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = 1.685312368 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = 1.685312368 + 0.08333333335
x = 1.685312368 + 0.08333333335

Combine like terms: 1.685312368 + 0.08333333335 = 1.76864570135
x = 1.76864570135

Simplifying
x = 1.76864570135


Subproblem 2
x + -0.08333333335 = -1.685312368

Simplifying
x + -0.08333333335 = -1.685312368

Reorder the terms:
-0.08333333335 + x = -1.685312368

Solving
-0.08333333335 + x = -1.685312368

Solving for variable 'x'.

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

Add '0.08333333335' to each side of the equation.
-0.08333333335 + 0.08333333335 + x = -1.685312368 + 0.08333333335

Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000
0.00000000000 + x = -1.685312368 + 0.08333333335
x = -1.685312368 + 0.08333333335

Combine like terms: -1.685312368 + 0.08333333335 = -1.60197903465
x = -1.60197903465

Simplifying
x = -1.60197903465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.76864570135, -1.60197903465}

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