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

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


Simplifying
5(2x + 4) + -2x(x + -2) = 0

Reorder the terms:
5(4 + 2x) + -2x(x + -2) = 0
(4 * 5 + 2x * 5) + -2x(x + -2) = 0
(20 + 10x) + -2x(x + -2) = 0

Reorder the terms:
20 + 10x + -2x(-2 + x) = 0
20 + 10x + (-2 * -2x + x * -2x) = 0
20 + 10x + (4x + -2x2) = 0

Combine like terms: 10x + 4x = 14x
20 + 14x + -2x2 = 0

Solving
20 + 14x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 7x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 7x + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + 7x + -1x2 = 0

Solving
10 + 7x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + -7x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -7x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -7x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -7x + x2 = 0 + 10
-7x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-7x + x2 = 10

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 10 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + -7x + x2 = 22.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
x + -3.5 = 4.716990566

Simplifying
x + -3.5 = 4.716990566

Reorder the terms:
-3.5 + x = 4.716990566

Solving
-3.5 + x = 4.716990566

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 4.716990566 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.716990566 + 3.5
x = 4.716990566 + 3.5

Combine like terms: 4.716990566 + 3.5 = 8.216990566
x = 8.216990566

Simplifying
x = 8.216990566


Subproblem 2
x + -3.5 = -4.716990566

Simplifying
x + -3.5 = -4.716990566

Reorder the terms:
-3.5 + x = -4.716990566

Solving
-3.5 + x = -4.716990566

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -4.716990566 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.716990566 + 3.5
x = -4.716990566 + 3.5

Combine like terms: -4.716990566 + 3.5 = -1.216990566
x = -1.216990566

Simplifying
x = -1.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.216990566, -1.216990566}
Solution
x = {8.216990566, -1.216990566}

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