3(x-2)(x+1)-4=

Solution for 3(x-2)(x+1)-4= equation:

Simplifying
3(x + -2)(x + 1) + -4 = 0

Reorder the terms:
3(-2 + x)(x + 1) + -4 = 0

Reorder the terms:
3(-2 + x)(1 + x) + -4 = 0

Multiply (-2 + x) * (1 + x)
3(-2(1 + x) + x(1 + x)) + -4 = 0
3((1 * -2 + x * -2) + x(1 + x)) + -4 = 0
3((-2 + -2x) + x(1 + x)) + -4 = 0
3(-2 + -2x + (1 * x + x * x)) + -4 = 0
3(-2 + -2x + (1x + x2)) + -4 = 0

Combine like terms: -2x + 1x = -1x
3(-2 + -1x + x2) + -4 = 0
(-2 * 3 + -1x * 3 + x2 * 3) + -4 = 0
(-6 + -3x + 3x2) + -4 = 0

Reorder the terms:
-6 + -4 + -3x + 3x2 = 0

Combine like terms: -6 + -4 = -10
-10 + -3x + 3x2 = 0

Solving
-10 + -3x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-3.333333333 + -1x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -1x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -1x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -1x + x2 = 0 + 3.333333333
-1x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-1x + x2 = 3.333333333

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 3.333333333 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3.333333333 + 0.25

Combine like terms: 3.333333333 + 0.25 = 3.583333333
0.25 + -1x + x2 = 3.583333333

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.583333333

Calculate the square root of the right side: 1.892969449

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.892969449 and -1.892969449.

Subproblem 1
x + -0.5 = 1.892969449

Simplifying
x + -0.5 = 1.892969449

Reorder the terms:
-0.5 + x = 1.892969449

Solving
-0.5 + x = 1.892969449

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.892969449 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.892969449 + 0.5
x = 1.892969449 + 0.5

Combine like terms: 1.892969449 + 0.5 = 2.392969449
x = 2.392969449

Simplifying
x = 2.392969449

Subproblem 2
x + -0.5 = -1.892969449

Simplifying
x + -0.5 = -1.892969449

Reorder the terms:
-0.5 + x = -1.892969449

Solving
-0.5 + x = -1.892969449

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.892969449 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.892969449 + 0.5
x = -1.892969449 + 0.5

Combine like terms: -1.892969449 + 0.5 = -1.392969449
x = -1.392969449

Simplifying
x = -1.392969449

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.392969449, -1.392969449}