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

Solution for 5(x+2)(x-1)=4+x equation:

Simplifying
5(x + 2)(x + -1) = 4 + x

Reorder the terms:
5(2 + x)(x + -1) = 4 + x

Reorder the terms:
5(2 + x)(-1 + x) = 4 + x

Multiply (2 + x) * (-1 + x)
5(2(-1 + x) + x(-1 + x)) = 4 + x
5((-1 * 2 + x * 2) + x(-1 + x)) = 4 + x
5((-2 + 2x) + x(-1 + x)) = 4 + x
5(-2 + 2x + (-1 * x + x * x)) = 4 + x
5(-2 + 2x + (-1x + x2)) = 4 + x

Combine like terms: 2x + -1x = 1x
5(-2 + 1x + x2) = 4 + x
(-2 * 5 + 1x * 5 + x2 * 5) = 4 + x
(-10 + 5x + 5x2) = 4 + x

Solving
-10 + 5x + 5x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
-10 + -4 + 5x + -1x + 5x2 = 4 + x + -4 + -1x

Combine like terms: -10 + -4 = -14
-14 + 5x + -1x + 5x2 = 4 + x + -4 + -1x

Combine like terms: 5x + -1x = 4x
-14 + 4x + 5x2 = 4 + x + -4 + -1x

Reorder the terms:
-14 + 4x + 5x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
-14 + 4x + 5x2 = 0 + x + -1x
-14 + 4x + 5x2 = x + -1x

Combine like terms: x + -1x = 0
-14 + 4x + 5x2 = 0

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

Divide each side by '5'.
-2.8 + 0.8x + x2 = 0

Move the constant term to the right:

Add '2.8' to each side of the equation.
-2.8 + 0.8x + 2.8 + x2 = 0 + 2.8

Reorder the terms:
-2.8 + 2.8 + 0.8x + x2 = 0 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
0.0 + 0.8x + x2 = 0 + 2.8
0.8x + x2 = 0 + 2.8

Combine like terms: 0 + 2.8 = 2.8
0.8x + x2 = 2.8

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 2.8 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 2.8 + 0.16

Combine like terms: 2.8 + 0.16 = 2.96
0.16 + 0.8x + x2 = 2.96

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 2.96

Calculate the square root of the right side: 1.720465053

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.720465053 and -1.720465053.

Subproblem 1
x + 0.4 = 1.720465053

Simplifying
x + 0.4 = 1.720465053

Reorder the terms:
0.4 + x = 1.720465053

Solving
0.4 + x = 1.720465053

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = 1.720465053 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = 1.720465053 + -0.4
x = 1.720465053 + -0.4

Combine like terms: 1.720465053 + -0.4 = 1.320465053
x = 1.320465053

Simplifying
x = 1.320465053

Subproblem 2
x + 0.4 = -1.720465053

Simplifying
x + 0.4 = -1.720465053

Reorder the terms:
0.4 + x = -1.720465053

Solving
0.4 + x = -1.720465053

Solving for variable 'x'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x = -1.720465053 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x = -1.720465053 + -0.4
x = -1.720465053 + -0.4

Combine like terms: -1.720465053 + -0.4 = -2.120465053
x = -2.120465053

Simplifying
x = -2.120465053

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.320465053, -2.120465053}