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

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

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

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

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

Multiply (-7 + x) * (-5 + 3x)
(-7(-5 + 3x) + x(-5 + 3x)) = (2x + 5)
((-5 * -7 + 3x * -7) + x(-5 + 3x)) = (2x + 5)
((35 + -21x) + x(-5 + 3x)) = (2x + 5)
(35 + -21x + (-5 * x + 3x * x)) = (2x + 5)
(35 + -21x + (-5x + 3x2)) = (2x + 5)

Combine like terms: -21x + -5x = -26x
(35 + -26x + 3x2) = (2x + 5)

Reorder the terms:
35 + -26x + 3x2 = (5 + 2x)

Remove parenthesis around (5 + 2x)
35 + -26x + 3x2 = 5 + 2x

Solving
35 + -26x + 3x2 = 5 + 2x

Solving for variable 'x'.

Reorder the terms:
35 + -5 + -26x + -2x + 3x2 = 5 + 2x + -5 + -2x

Combine like terms: 35 + -5 = 30
30 + -26x + -2x + 3x2 = 5 + 2x + -5 + -2x

Combine like terms: -26x + -2x = -28x
30 + -28x + 3x2 = 5 + 2x + -5 + -2x

Reorder the terms:
30 + -28x + 3x2 = 5 + -5 + 2x + -2x

Combine like terms: 5 + -5 = 0
30 + -28x + 3x2 = 0 + 2x + -2x
30 + -28x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
30 + -28x + 3x2 = 0

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

Divide each side by '3'.
10 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -9.333333333x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -9.333333333x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -9.333333333x + x2 = 0 + -10
-9.333333333x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-9.333333333x + x2 = -10

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = -10 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = -10 + 21.77777778

Combine like terms: -10 + 21.77777778 = 11.77777778
21.77777778 + -9.333333333x + x2 = 11.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 11.77777778

Calculate the square root of the right side: 3.431876714

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 3.431876714 and -3.431876714.

Subproblem 1
x + -4.666666667 = 3.431876714

Simplifying
x + -4.666666667 = 3.431876714

Reorder the terms:
-4.666666667 + x = 3.431876714

Solving
-4.666666667 + x = 3.431876714

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 3.431876714 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 3.431876714 + 4.666666667
x = 3.431876714 + 4.666666667

Combine like terms: 3.431876714 + 4.666666667 = 8.098543381
x = 8.098543381

Simplifying
x = 8.098543381

Subproblem 2
x + -4.666666667 = -3.431876714

Simplifying
x + -4.666666667 = -3.431876714

Reorder the terms:
-4.666666667 + x = -3.431876714

Solving
-4.666666667 + x = -3.431876714

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -3.431876714 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -3.431876714 + 4.666666667
x = -3.431876714 + 4.666666667

Combine like terms: -3.431876714 + 4.666666667 = 1.234789953
x = 1.234789953

Simplifying
x = 1.234789953

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.098543381, 1.234789953}