(x+1)(2x-5)=(10x-3)(7-2x)

Solution for (x+1)(2x-5)=(10x-3)(7-2x) equation:

Simplifying
(x + 1)(2x + -5) = (10x + -3)(7 + -2x)

Reorder the terms:
(1 + x)(2x + -5) = (10x + -3)(7 + -2x)

Reorder the terms:
(1 + x)(-5 + 2x) = (10x + -3)(7 + -2x)

Multiply (1 + x) * (-5 + 2x)
(1(-5 + 2x) + x(-5 + 2x)) = (10x + -3)(7 + -2x)
((-5 * 1 + 2x * 1) + x(-5 + 2x)) = (10x + -3)(7 + -2x)
((-5 + 2x) + x(-5 + 2x)) = (10x + -3)(7 + -2x)
(-5 + 2x + (-5 * x + 2x * x)) = (10x + -3)(7 + -2x)
(-5 + 2x + (-5x + 2x2)) = (10x + -3)(7 + -2x)

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

Reorder the terms:
-5 + -3x + 2x2 = (-3 + 10x)(7 + -2x)

Multiply (-3 + 10x) * (7 + -2x)
-5 + -3x + 2x2 = (-3(7 + -2x) + 10x * (7 + -2x))
-5 + -3x + 2x2 = ((7 * -3 + -2x * -3) + 10x * (7 + -2x))
-5 + -3x + 2x2 = ((-21 + 6x) + 10x * (7 + -2x))
-5 + -3x + 2x2 = (-21 + 6x + (7 * 10x + -2x * 10x))
-5 + -3x + 2x2 = (-21 + 6x + (70x + -20x2))

Combine like terms: 6x + 70x = 76x
-5 + -3x + 2x2 = (-21 + 76x + -20x2)

Solving
-5 + -3x + 2x2 = -21 + 76x + -20x2

Solving for variable 'x'.

Reorder the terms:
-5 + 21 + -3x + -76x + 2x2 + 20x2 = -21 + 76x + -20x2 + 21 + -76x + 20x2

Combine like terms: -5 + 21 = 16
16 + -3x + -76x + 2x2 + 20x2 = -21 + 76x + -20x2 + 21 + -76x + 20x2

Combine like terms: -3x + -76x = -79x
16 + -79x + 2x2 + 20x2 = -21 + 76x + -20x2 + 21 + -76x + 20x2

Combine like terms: 2x2 + 20x2 = 22x2
16 + -79x + 22x2 = -21 + 76x + -20x2 + 21 + -76x + 20x2

Reorder the terms:
16 + -79x + 22x2 = -21 + 21 + 76x + -76x + -20x2 + 20x2

Combine like terms: -21 + 21 = 0
16 + -79x + 22x2 = 0 + 76x + -76x + -20x2 + 20x2
16 + -79x + 22x2 = 76x + -76x + -20x2 + 20x2

Combine like terms: 76x + -76x = 0
16 + -79x + 22x2 = 0 + -20x2 + 20x2
16 + -79x + 22x2 = -20x2 + 20x2

Combine like terms: -20x2 + 20x2 = 0
16 + -79x + 22x2 = 0

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

Divide each side by '22'.
0.7272727273 + -3.590909091x + x2 = 0

Move the constant term to the right:

Add '-0.7272727273' to each side of the equation.
0.7272727273 + -3.590909091x + -0.7272727273 + x2 = 0 + -0.7272727273

Reorder the terms:
0.7272727273 + -0.7272727273 + -3.590909091x + x2 = 0 + -0.7272727273

Combine like terms: 0.7272727273 + -0.7272727273 = 0.0000000000
0.0000000000 + -3.590909091x + x2 = 0 + -0.7272727273
-3.590909091x + x2 = 0 + -0.7272727273

Combine like terms: 0 + -0.7272727273 = -0.7272727273
-3.590909091x + x2 = -0.7272727273

The x term is -3.590909091x.  Take half its coefficient (-1.795454546).
Square it (3.223657027) and add it to both sides.

Add '3.223657027' to each side of the equation.
-3.590909091x + 3.223657027 + x2 = -0.7272727273 + 3.223657027

Reorder the terms:
3.223657027 + -3.590909091x + x2 = -0.7272727273 + 3.223657027

Combine like terms: -0.7272727273 + 3.223657027 = 2.4963842997
3.223657027 + -3.590909091x + x2 = 2.4963842997

Factor a perfect square on the left side:
(x + -1.795454546)(x + -1.795454546) = 2.4963842997

Calculate the square root of the right side: 1.579995032

Break this problem into two subproblems by setting 
(x + -1.795454546) equal to 1.579995032 and -1.579995032.

Subproblem 1
x + -1.795454546 = 1.579995032

Simplifying
x + -1.795454546 = 1.579995032

Reorder the terms:
-1.795454546 + x = 1.579995032

Solving
-1.795454546 + x = 1.579995032

Solving for variable 'x'.

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

Add '1.795454546' to each side of the equation.
-1.795454546 + 1.795454546 + x = 1.579995032 + 1.795454546

Combine like terms: -1.795454546 + 1.795454546 = 0.000000000
0.000000000 + x = 1.579995032 + 1.795454546
x = 1.579995032 + 1.795454546

Combine like terms: 1.579995032 + 1.795454546 = 3.375449578
x = 3.375449578

Simplifying
x = 3.375449578

Subproblem 2
x + -1.795454546 = -1.579995032

Simplifying
x + -1.795454546 = -1.579995032

Reorder the terms:
-1.795454546 + x = -1.579995032

Solving
-1.795454546 + x = -1.579995032

Solving for variable 'x'.

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

Add '1.795454546' to each side of the equation.
-1.795454546 + 1.795454546 + x = -1.579995032 + 1.795454546

Combine like terms: -1.795454546 + 1.795454546 = 0.000000000
0.000000000 + x = -1.579995032 + 1.795454546
x = -1.579995032 + 1.795454546

Combine like terms: -1.579995032 + 1.795454546 = 0.215459514
x = 0.215459514

Simplifying
x = 0.215459514

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.375449578, 0.215459514}