(2x-5)(7x)=(4x+1)(x-3)

Solution for (2x-5)(7x)=(4x+1)(x-3) equation:

Simplifying
(2x + -5)(7x) = (4x + 1)(x + -3)

Reorder the terms:
(-5 + 2x)(7x) = (4x + 1)(x + -3)

Remove parenthesis around (7x)
(-5 + 2x) * 7x = (4x + 1)(x + -3)

Reorder the terms for easier multiplication:
7x(-5 + 2x) = (4x + 1)(x + -3)
(-5 * 7x + 2x * 7x) = (4x + 1)(x + -3)
(-35x + 14x2) = (4x + 1)(x + -3)

Reorder the terms:
-35x + 14x2 = (1 + 4x)(x + -3)

Reorder the terms:
-35x + 14x2 = (1 + 4x)(-3 + x)

Multiply (1 + 4x) * (-3 + x)
-35x + 14x2 = (1(-3 + x) + 4x * (-3 + x))
-35x + 14x2 = ((-3 * 1 + x * 1) + 4x * (-3 + x))
-35x + 14x2 = ((-3 + 1x) + 4x * (-3 + x))
-35x + 14x2 = (-3 + 1x + (-3 * 4x + x * 4x))
-35x + 14x2 = (-3 + 1x + (-12x + 4x2))

Combine like terms: 1x + -12x = -11x
-35x + 14x2 = (-3 + -11x + 4x2)

Solving
-35x + 14x2 = -3 + -11x + 4x2

Solving for variable 'x'.

Reorder the terms:
3 + -35x + 11x + 14x2 + -4x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2

Combine like terms: -35x + 11x = -24x
3 + -24x + 14x2 + -4x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2

Combine like terms: 14x2 + -4x2 = 10x2
3 + -24x + 10x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2

Reorder the terms:
3 + -24x + 10x2 = -3 + 3 + -11x + 11x + 4x2 + -4x2

Combine like terms: -3 + 3 = 0
3 + -24x + 10x2 = 0 + -11x + 11x + 4x2 + -4x2
3 + -24x + 10x2 = -11x + 11x + 4x2 + -4x2

Combine like terms: -11x + 11x = 0
3 + -24x + 10x2 = 0 + 4x2 + -4x2
3 + -24x + 10x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3 + -24x + 10x2 = 0

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

Divide each side by '10'.
0.3 + -2.4x + x2 = 0.0

Move the constant term to the right:

Add '-0.3' to each side of the equation.
0.3 + -2.4x + -0.3 + x2 = 0.0 + -0.3

Reorder the terms:
0.3 + -0.3 + -2.4x + x2 = 0.0 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + -2.4x + x2 = 0.0 + -0.3
-2.4x + x2 = 0.0 + -0.3

Combine like terms: 0.0 + -0.3 = -0.3
-2.4x + x2 = -0.3

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = -0.3 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = -0.3 + 1.44

Combine like terms: -0.3 + 1.44 = 1.14
1.44 + -2.4x + x2 = 1.14

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 1.14

Calculate the square root of the right side: 1.067707825

Break this problem into two subproblems by setting 
(x + -1.2) equal to 1.067707825 and -1.067707825.

Subproblem 1
x + -1.2 = 1.067707825

Simplifying
x + -1.2 = 1.067707825

Reorder the terms:
-1.2 + x = 1.067707825

Solving
-1.2 + x = 1.067707825

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = 1.067707825 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = 1.067707825 + 1.2
x = 1.067707825 + 1.2

Combine like terms: 1.067707825 + 1.2 = 2.267707825
x = 2.267707825

Simplifying
x = 2.267707825

Subproblem 2
x + -1.2 = -1.067707825

Simplifying
x + -1.2 = -1.067707825

Reorder the terms:
-1.2 + x = -1.067707825

Solving
-1.2 + x = -1.067707825

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = -1.067707825 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = -1.067707825 + 1.2
x = -1.067707825 + 1.2

Combine like terms: -1.067707825 + 1.2 = 0.132292175
x = 0.132292175

Simplifying
x = 0.132292175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.267707825, 0.132292175}