(2x-3)(x-1)=x(4x+3)+10

Solution for (2x-3)(x-1)=x(4x+3)+10 equation:

Simplifying
(2x + -3)(x + -1) = x(4x + 3) + 10

Reorder the terms:
(-3 + 2x)(x + -1) = x(4x + 3) + 10

Reorder the terms:
(-3 + 2x)(-1 + x) = x(4x + 3) + 10

Multiply (-3 + 2x) * (-1 + x)
(-3(-1 + x) + 2x * (-1 + x)) = x(4x + 3) + 10
((-1 * -3 + x * -3) + 2x * (-1 + x)) = x(4x + 3) + 10
((3 + -3x) + 2x * (-1 + x)) = x(4x + 3) + 10
(3 + -3x + (-1 * 2x + x * 2x)) = x(4x + 3) + 10
(3 + -3x + (-2x + 2x2)) = x(4x + 3) + 10

Combine like terms: -3x + -2x = -5x
(3 + -5x + 2x2) = x(4x + 3) + 10

Reorder the terms:
3 + -5x + 2x2 = x(3 + 4x) + 10
3 + -5x + 2x2 = (3 * x + 4x * x) + 10
3 + -5x + 2x2 = (3x + 4x2) + 10

Reorder the terms:
3 + -5x + 2x2 = 10 + 3x + 4x2

Solving
3 + -5x + 2x2 = 10 + 3x + 4x2

Solving for variable 'x'.

Reorder the terms:
3 + -10 + -5x + -3x + 2x2 + -4x2 = 10 + 3x + 4x2 + -10 + -3x + -4x2

Combine like terms: 3 + -10 = -7
-7 + -5x + -3x + 2x2 + -4x2 = 10 + 3x + 4x2 + -10 + -3x + -4x2

Combine like terms: -5x + -3x = -8x
-7 + -8x + 2x2 + -4x2 = 10 + 3x + 4x2 + -10 + -3x + -4x2

Combine like terms: 2x2 + -4x2 = -2x2
-7 + -8x + -2x2 = 10 + 3x + 4x2 + -10 + -3x + -4x2

Reorder the terms:
-7 + -8x + -2x2 = 10 + -10 + 3x + -3x + 4x2 + -4x2

Combine like terms: 10 + -10 = 0
-7 + -8x + -2x2 = 0 + 3x + -3x + 4x2 + -4x2
-7 + -8x + -2x2 = 3x + -3x + 4x2 + -4x2

Combine like terms: 3x + -3x = 0
-7 + -8x + -2x2 = 0 + 4x2 + -4x2
-7 + -8x + -2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-7 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 8x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 8x + 2x2)' equal to zero and attempt to solve:

Simplifying
7 + 8x + 2x2 = 0

Solving
7 + 8x + 2x2 = 0

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

Divide each side by '2'.
3.5 + 4x + x2 = 0

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + 4x + -3.5 + x2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + 4x + x2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + 4x + x2 = 0 + -3.5
4x + x2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
4x + x2 = -3.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -3.5 + 4

Reorder the terms:
4 + 4x + x2 = -3.5 + 4

Combine like terms: -3.5 + 4 = 0.5
4 + 4x + x2 = 0.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(x + 2) equal to 0.707106781 and -0.707106781.

Subproblem 1
x + 2 = 0.707106781

Simplifying
x + 2 = 0.707106781

Reorder the terms:
2 + x = 0.707106781

Solving
2 + x = 0.707106781

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 0.707106781 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0.707106781 + -2
x = 0.707106781 + -2

Combine like terms: 0.707106781 + -2 = -1.292893219
x = -1.292893219

Simplifying
x = -1.292893219

Subproblem 2
x + 2 = -0.707106781

Simplifying
x + 2 = -0.707106781

Reorder the terms:
2 + x = -0.707106781

Solving
2 + x = -0.707106781

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -0.707106781 + -2

Combine like terms: 2 + -2 = 0
0 + x = -0.707106781 + -2
x = -0.707106781 + -2

Combine like terms: -0.707106781 + -2 = -2.707106781
x = -2.707106781

Simplifying
x = -2.707106781

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.292893219, -2.707106781}
Solution
x = {-1.292893219, -2.707106781}