(5x-10)(x+6)=10

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Solution for (5x-10)(x+6)=10 equation: 


Simplifying
(5x + -10)(x + 6) = 10

Reorder the terms:
(-10 + 5x)(x + 6) = 10

Reorder the terms:
(-10 + 5x)(6 + x) = 10

Multiply (-10 + 5x) * (6 + x)
(-10(6 + x) + 5x * (6 + x)) = 10
((6 * -10 + x * -10) + 5x * (6 + x)) = 10
((-60 + -10x) + 5x * (6 + x)) = 10
(-60 + -10x + (6 * 5x + x * 5x)) = 10
(-60 + -10x + (30x + 5x2)) = 10

Combine like terms: -10x + 30x = 20x
(-60 + 20x + 5x2) = 10

Solving
-60 + 20x + 5x2 = 10

Solving for variable 'x'.

Reorder the terms:
-60 + -10 + 20x + 5x2 = 10 + -10

Combine like terms: -60 + -10 = -70
-70 + 20x + 5x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-70 + 20x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-14 + 4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-14 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-14 + 4x + x2 = 0

Solving
-14 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 4x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 4x + x2 = 0 + 14

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

Combine like terms: 0 + 14 = 14
4x + x2 = 14

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 14 + 4

Reorder the terms:
4 + 4x + x2 = 14 + 4

Combine like terms: 14 + 4 = 18
4 + 4x + x2 = 18

Factor a perfect square on the left side:
(x + 2)(x + 2) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 2) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 2 = 4.242640687

Simplifying
x + 2 = 4.242640687

Reorder the terms:
2 + x = 4.242640687

Solving
2 + x = 4.242640687

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 4.242640687 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.242640687 + -2
x = 4.242640687 + -2

Combine like terms: 4.242640687 + -2 = 2.242640687
x = 2.242640687

Simplifying
x = 2.242640687


Subproblem 2
x + 2 = -4.242640687

Simplifying
x + 2 = -4.242640687

Reorder the terms:
2 + x = -4.242640687

Solving
2 + x = -4.242640687

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -4.242640687 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.242640687 + -2
x = -4.242640687 + -2

Combine like terms: -4.242640687 + -2 = -6.242640687
x = -6.242640687

Simplifying
x = -6.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.242640687, -6.242640687}
Solution
x = {2.242640687, -6.242640687}

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