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

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

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

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

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

Multiply (-5 + x) * (1 + 2x)
3(-5(1 + 2x) + x(1 + 2x)) = 3 + -1x
3((1 * -5 + 2x * -5) + x(1 + 2x)) = 3 + -1x
3((-5 + -10x) + x(1 + 2x)) = 3 + -1x
3(-5 + -10x + (1 * x + 2x * x)) = 3 + -1x
3(-5 + -10x + (1x + 2x2)) = 3 + -1x

Combine like terms: -10x + 1x = -9x
3(-5 + -9x + 2x2) = 3 + -1x
(-5 * 3 + -9x * 3 + 2x2 * 3) = 3 + -1x
(-15 + -27x + 6x2) = 3 + -1x

Solving
-15 + -27x + 6x2 = 3 + -1x

Solving for variable 'x'.

Reorder the terms:
-15 + -3 + -27x + x + 6x2 = 3 + -1x + -3 + x

Combine like terms: -15 + -3 = -18
-18 + -27x + x + 6x2 = 3 + -1x + -3 + x

Combine like terms: -27x + x = -26x
-18 + -26x + 6x2 = 3 + -1x + -3 + x

Reorder the terms:
-18 + -26x + 6x2 = 3 + -3 + -1x + x

Combine like terms: 3 + -3 = 0
-18 + -26x + 6x2 = 0 + -1x + x
-18 + -26x + 6x2 = -1x + x

Combine like terms: -1x + x = 0
-18 + -26x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + -13x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-9 + -13x + 3x2)' equal to zero and attempt to solve:

Simplifying
-9 + -13x + 3x2 = 0

Solving
-9 + -13x + 3x2 = 0

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

Divide each side by '3'.
-3 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4.333333333x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -4.333333333x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4.333333333x + x2 = 0 + 3
-4.333333333x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4.333333333x + x2 = 3

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 3 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 3 + 4.694444446

Combine like terms: 3 + 4.694444446 = 7.694444446
4.694444446 + -4.333333333x + x2 = 7.694444446

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 7.694444446

Calculate the square root of the right side: 2.773886163

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 2.773886163 and -2.773886163.

Subproblem 1
x + -2.166666667 = 2.773886163

Simplifying
x + -2.166666667 = 2.773886163

Reorder the terms:
-2.166666667 + x = 2.773886163

Solving
-2.166666667 + x = 2.773886163

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 2.773886163 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 2.773886163 + 2.166666667
x = 2.773886163 + 2.166666667

Combine like terms: 2.773886163 + 2.166666667 = 4.94055283
x = 4.94055283

Simplifying
x = 4.94055283

Subproblem 2
x + -2.166666667 = -2.773886163

Simplifying
x + -2.166666667 = -2.773886163

Reorder the terms:
-2.166666667 + x = -2.773886163

Solving
-2.166666667 + x = -2.773886163

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -2.773886163 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -2.773886163 + 2.166666667
x = -2.773886163 + 2.166666667

Combine like terms: -2.773886163 + 2.166666667 = -0.607219496
x = -0.607219496

Simplifying
x = -0.607219496

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.94055283, -0.607219496}
Solution
x = {4.94055283, -0.607219496}