5x*3(x-1)=7x-2

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

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

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

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

Multiply 5 * 3
15x(-1 + x) = 7x + -2
(-1 * 15x + x * 15x) = 7x + -2
(-15x + 15x2) = 7x + -2

Reorder the terms:
-15x + 15x2 = -2 + 7x

Solving
-15x + 15x2 = -2 + 7x

Solving for variable 'x'.

Reorder the terms:
2 + -15x + -7x + 15x2 = -2 + 7x + 2 + -7x

Combine like terms: -15x + -7x = -22x
2 + -22x + 15x2 = -2 + 7x + 2 + -7x

Reorder the terms:
2 + -22x + 15x2 = -2 + 2 + 7x + -7x

Combine like terms: -2 + 2 = 0
2 + -22x + 15x2 = 0 + 7x + -7x
2 + -22x + 15x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
2 + -22x + 15x2 = 0

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

Divide each side by '15'.
0.1333333333 + -1.466666667x + x2 = 0

Move the constant term to the right:

Add '-0.1333333333' to each side of the equation.
0.1333333333 + -1.466666667x + -0.1333333333 + x2 = 0 + -0.1333333333

Reorder the terms:
0.1333333333 + -0.1333333333 + -1.466666667x + x2 = 0 + -0.1333333333

Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000
0.0000000000 + -1.466666667x + x2 = 0 + -0.1333333333
-1.466666667x + x2 = 0 + -0.1333333333

Combine like terms: 0 + -0.1333333333 = -0.1333333333
-1.466666667x + x2 = -0.1333333333

The x term is -1.466666667x.  Take half its coefficient (-0.7333333335).
Square it (0.5377777780) and add it to both sides.

Add '0.5377777780' to each side of the equation.
-1.466666667x + 0.5377777780 + x2 = -0.1333333333 + 0.5377777780

Reorder the terms:
0.5377777780 + -1.466666667x + x2 = -0.1333333333 + 0.5377777780

Combine like terms: -0.1333333333 + 0.5377777780 = 0.4044444447
0.5377777780 + -1.466666667x + x2 = 0.4044444447

Factor a perfect square on the left side:
(x + -0.7333333335)(x + -0.7333333335) = 0.4044444447

Calculate the square root of the right side: 0.635959468

Break this problem into two subproblems by setting 
(x + -0.7333333335) equal to 0.635959468 and -0.635959468.

Subproblem 1
x + -0.7333333335 = 0.635959468

Simplifying
x + -0.7333333335 = 0.635959468

Reorder the terms:
-0.7333333335 + x = 0.635959468

Solving
-0.7333333335 + x = 0.635959468

Solving for variable 'x'.

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

Add '0.7333333335' to each side of the equation.
-0.7333333335 + 0.7333333335 + x = 0.635959468 + 0.7333333335

Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000
0.0000000000 + x = 0.635959468 + 0.7333333335
x = 0.635959468 + 0.7333333335

Combine like terms: 0.635959468 + 0.7333333335 = 1.3692928015
x = 1.3692928015

Simplifying
x = 1.3692928015

Subproblem 2
x + -0.7333333335 = -0.635959468

Simplifying
x + -0.7333333335 = -0.635959468

Reorder the terms:
-0.7333333335 + x = -0.635959468

Solving
-0.7333333335 + x = -0.635959468

Solving for variable 'x'.

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

Add '0.7333333335' to each side of the equation.
-0.7333333335 + 0.7333333335 + x = -0.635959468 + 0.7333333335

Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000
0.0000000000 + x = -0.635959468 + 0.7333333335
x = -0.635959468 + 0.7333333335

Combine like terms: -0.635959468 + 0.7333333335 = 0.0973738655
x = 0.0973738655

Simplifying
x = 0.0973738655

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3692928015, 0.0973738655}