2x(x+4)=4(5-3x)

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Solution for 2x(x+4)=4(5-3x) equation:


Simplifying
2x(x + 4) = 4(5 + -3x)

Reorder the terms:
2x(4 + x) = 4(5 + -3x)
(4 * 2x + x * 2x) = 4(5 + -3x)
(8x + 2x2) = 4(5 + -3x)
8x + 2x2 = (5 * 4 + -3x * 4)
8x + 2x2 = (20 + -12x)

Solving
8x + 2x2 = 20 + -12x

Solving for variable 'x'.

Reorder the terms:
-20 + 8x + 12x + 2x2 = 20 + -12x + -20 + 12x

Combine like terms: 8x + 12x = 20x
-20 + 20x + 2x2 = 20 + -12x + -20 + 12x

Reorder the terms:
-20 + 20x + 2x2 = 20 + -20 + -12x + 12x

Combine like terms: 20 + -20 = 0
-20 + 20x + 2x2 = 0 + -12x + 12x
-20 + 20x + 2x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-20 + 20x + 2x2 = 0

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

Ignore the factor 2.

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

Simplifying
-10 + 10x + x2 = 0

Solving
-10 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 10 + 25

Reorder the terms:
25 + 10x + x2 = 10 + 25

Combine like terms: 10 + 25 = 35
25 + 10x + x2 = 35

Factor a perfect square on the left side:
(x + 5)(x + 5) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(x + 5) equal to 5.916079783 and -5.916079783.


Subproblem 1
x + 5 = 5.916079783

Simplifying
x + 5 = 5.916079783

Reorder the terms:
5 + x = 5.916079783

Solving
5 + x = 5.916079783

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 5.916079783 + -5

Combine like terms: 5 + -5 = 0
0 + x = 5.916079783 + -5
x = 5.916079783 + -5

Combine like terms: 5.916079783 + -5 = 0.916079783
x = 0.916079783

Simplifying
x = 0.916079783


Subproblem 2
x + 5 = -5.916079783

Simplifying
x + 5 = -5.916079783

Reorder the terms:
5 + x = -5.916079783

Solving
5 + x = -5.916079783

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -5.916079783 + -5

Combine like terms: 5 + -5 = 0
0 + x = -5.916079783 + -5
x = -5.916079783 + -5

Combine like terms: -5.916079783 + -5 = -10.916079783
x = -10.916079783

Simplifying
x = -10.916079783


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.916079783, -10.916079783}
Solution
x = {0.916079783, -10.916079783}

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