(5x-2)(3x-7)=-9x+3

Solution for (5x-2)(3x-7)=-9x+3 equation:

Simplifying
(5x + -2)(3x + -7) = -9x + 3

Reorder the terms:
(-2 + 5x)(3x + -7) = -9x + 3

Reorder the terms:
(-2 + 5x)(-7 + 3x) = -9x + 3

Multiply (-2 + 5x) * (-7 + 3x)
(-2(-7 + 3x) + 5x * (-7 + 3x)) = -9x + 3
((-7 * -2 + 3x * -2) + 5x * (-7 + 3x)) = -9x + 3
((14 + -6x) + 5x * (-7 + 3x)) = -9x + 3
(14 + -6x + (-7 * 5x + 3x * 5x)) = -9x + 3
(14 + -6x + (-35x + 15x2)) = -9x + 3

Combine like terms: -6x + -35x = -41x
(14 + -41x + 15x2) = -9x + 3

Reorder the terms:
14 + -41x + 15x2 = 3 + -9x

Solving
14 + -41x + 15x2 = 3 + -9x

Solving for variable 'x'.

Reorder the terms:
14 + -3 + -41x + 9x + 15x2 = 3 + -9x + -3 + 9x

Combine like terms: 14 + -3 = 11
11 + -41x + 9x + 15x2 = 3 + -9x + -3 + 9x

Combine like terms: -41x + 9x = -32x
11 + -32x + 15x2 = 3 + -9x + -3 + 9x

Reorder the terms:
11 + -32x + 15x2 = 3 + -3 + -9x + 9x

Combine like terms: 3 + -3 = 0
11 + -32x + 15x2 = 0 + -9x + 9x
11 + -32x + 15x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
11 + -32x + 15x2 = 0

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

Divide each side by '15'.
0.7333333333 + -2.133333333x + x2 = 0

Move the constant term to the right:

Add '-0.7333333333' to each side of the equation.
0.7333333333 + -2.133333333x + -0.7333333333 + x2 = 0 + -0.7333333333

Reorder the terms:
0.7333333333 + -0.7333333333 + -2.133333333x + x2 = 0 + -0.7333333333

Combine like terms: 0.7333333333 + -0.7333333333 = 0.0000000000
0.0000000000 + -2.133333333x + x2 = 0 + -0.7333333333
-2.133333333x + x2 = 0 + -0.7333333333

Combine like terms: 0 + -0.7333333333 = -0.7333333333
-2.133333333x + x2 = -0.7333333333

The x term is -2.133333333x.  Take half its coefficient (-1.066666667).
Square it (1.137777778) and add it to both sides.

Add '1.137777778' to each side of the equation.
-2.133333333x + 1.137777778 + x2 = -0.7333333333 + 1.137777778

Reorder the terms:
1.137777778 + -2.133333333x + x2 = -0.7333333333 + 1.137777778

Combine like terms: -0.7333333333 + 1.137777778 = 0.4044444447
1.137777778 + -2.133333333x + x2 = 0.4044444447

Factor a perfect square on the left side:
(x + -1.066666667)(x + -1.066666667) = 0.4044444447

Calculate the square root of the right side: 0.635959468

Break this problem into two subproblems by setting 
(x + -1.066666667) equal to 0.635959468 and -0.635959468.

Subproblem 1
x + -1.066666667 = 0.635959468

Simplifying
x + -1.066666667 = 0.635959468

Reorder the terms:
-1.066666667 + x = 0.635959468

Solving
-1.066666667 + x = 0.635959468

Solving for variable 'x'.

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

Add '1.066666667' to each side of the equation.
-1.066666667 + 1.066666667 + x = 0.635959468 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + x = 0.635959468 + 1.066666667
x = 0.635959468 + 1.066666667

Combine like terms: 0.635959468 + 1.066666667 = 1.702626135
x = 1.702626135

Simplifying
x = 1.702626135

Subproblem 2
x + -1.066666667 = -0.635959468

Simplifying
x + -1.066666667 = -0.635959468

Reorder the terms:
-1.066666667 + x = -0.635959468

Solving
-1.066666667 + x = -0.635959468

Solving for variable 'x'.

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

Add '1.066666667' to each side of the equation.
-1.066666667 + 1.066666667 + x = -0.635959468 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + x = -0.635959468 + 1.066666667
x = -0.635959468 + 1.066666667

Combine like terms: -0.635959468 + 1.066666667 = 0.430707199
x = 0.430707199

Simplifying
x = 0.430707199

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.702626135, 0.430707199}