3x*5(x-2)=-4+2x-2

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

Simplifying
3x * 5(x + -2) = -4 + 2x + -2

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

Reorder the terms for easier multiplication:
3 * 5x(-2 + x) = -4 + 2x + -2

Multiply 3 * 5
15x(-2 + x) = -4 + 2x + -2
(-2 * 15x + x * 15x) = -4 + 2x + -2
(-30x + 15x2) = -4 + 2x + -2

Reorder the terms:
-30x + 15x2 = -4 + -2 + 2x

Combine like terms: -4 + -2 = -6
-30x + 15x2 = -6 + 2x

Solving
-30x + 15x2 = -6 + 2x

Solving for variable 'x'.

Reorder the terms:
6 + -30x + -2x + 15x2 = -6 + 2x + 6 + -2x

Combine like terms: -30x + -2x = -32x
6 + -32x + 15x2 = -6 + 2x + 6 + -2x

Reorder the terms:
6 + -32x + 15x2 = -6 + 6 + 2x + -2x

Combine like terms: -6 + 6 = 0
6 + -32x + 15x2 = 0 + 2x + -2x
6 + -32x + 15x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
6 + -32x + 15x2 = 0

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

Divide each side by '15'.
0.4 + -2.133333333x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + -2.133333333x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + -2.133333333x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + -2.133333333x + x2 = 0 + -0.4
-2.133333333x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
-2.133333333x + x2 = -0.4

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 = -0.4 + 1.137777778

Reorder the terms:
1.137777778 + -2.133333333x + x2 = -0.4 + 1.137777778

Combine like terms: -0.4 + 1.137777778 = 0.737777778
1.137777778 + -2.133333333x + x2 = 0.737777778

Factor a perfect square on the left side:
(x + -1.066666667)(x + -1.066666667) = 0.737777778

Calculate the square root of the right side: 0.858939915

Break this problem into two subproblems by setting 
(x + -1.066666667) equal to 0.858939915 and -0.858939915.

Subproblem 1
x + -1.066666667 = 0.858939915

Simplifying
x + -1.066666667 = 0.858939915

Reorder the terms:
-1.066666667 + x = 0.858939915

Solving
-1.066666667 + x = 0.858939915

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 = 0.858939915 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + x = 0.858939915 + 1.066666667
x = 0.858939915 + 1.066666667

Combine like terms: 0.858939915 + 1.066666667 = 1.925606582
x = 1.925606582

Simplifying
x = 1.925606582

Subproblem 2
x + -1.066666667 = -0.858939915

Simplifying
x + -1.066666667 = -0.858939915

Reorder the terms:
-1.066666667 + x = -0.858939915

Solving
-1.066666667 + x = -0.858939915

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 = -0.858939915 + 1.066666667

Combine like terms: -1.066666667 + 1.066666667 = 0.000000000
0.000000000 + x = -0.858939915 + 1.066666667
x = -0.858939915 + 1.066666667

Combine like terms: -0.858939915 + 1.066666667 = 0.207726752
x = 0.207726752

Simplifying
x = 0.207726752

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.925606582, 0.207726752}