(2x+5)(x-1)=6

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Solution for (2x+5)(x-1)=6 equation: 


Simplifying
(2x + 5)(x + -1) = 6

Reorder the terms:
(5 + 2x)(x + -1) = 6

Reorder the terms:
(5 + 2x)(-1 + x) = 6

Multiply (5 + 2x) * (-1 + x)
(5(-1 + x) + 2x * (-1 + x)) = 6
((-1 * 5 + x * 5) + 2x * (-1 + x)) = 6
((-5 + 5x) + 2x * (-1 + x)) = 6
(-5 + 5x + (-1 * 2x + x * 2x)) = 6
(-5 + 5x + (-2x + 2x2)) = 6

Combine like terms: 5x + -2x = 3x
(-5 + 3x + 2x2) = 6

Solving
-5 + 3x + 2x2 = 6

Solving for variable 'x'.

Reorder the terms:
-5 + -6 + 3x + 2x2 = 6 + -6

Combine like terms: -5 + -6 = -11
-11 + 3x + 2x2 = 6 + -6

Combine like terms: 6 + -6 = 0
-11 + 3x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + 1.5x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + 1.5x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + 1.5x + x2 = 0 + 5.5
1.5x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
1.5x + x2 = 5.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 5.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 5.5 + 0.5625

Combine like terms: 5.5 + 0.5625 = 6.0625
0.5625 + 1.5x + x2 = 6.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 6.0625

Calculate the square root of the right side: 2.46221445

Break this problem into two subproblems by setting 
(x + 0.75) equal to 2.46221445 and -2.46221445.


Subproblem 1
x + 0.75 = 2.46221445

Simplifying
x + 0.75 = 2.46221445

Reorder the terms:
0.75 + x = 2.46221445

Solving
0.75 + x = 2.46221445

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 2.46221445 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 2.46221445 + -0.75
x = 2.46221445 + -0.75

Combine like terms: 2.46221445 + -0.75 = 1.71221445
x = 1.71221445

Simplifying
x = 1.71221445


Subproblem 2
x + 0.75 = -2.46221445

Simplifying
x + 0.75 = -2.46221445

Reorder the terms:
0.75 + x = -2.46221445

Solving
0.75 + x = -2.46221445

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -2.46221445 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -2.46221445 + -0.75
x = -2.46221445 + -0.75

Combine like terms: -2.46221445 + -0.75 = -3.21221445
x = -3.21221445

Simplifying
x = -3.21221445


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.71221445, -3.21221445}

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