5(x+4)-x(2x-3)=0

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Solution for 5(x+4)-x(2x-3)=0 equation: 


Simplifying
5(x + 4) + -1x(2x + -3) = 0

Reorder the terms:
5(4 + x) + -1x(2x + -3) = 0
(4 * 5 + x * 5) + -1x(2x + -3) = 0
(20 + 5x) + -1x(2x + -3) = 0

Reorder the terms:
20 + 5x + -1x(-3 + 2x) = 0
20 + 5x + (-3 * -1x + 2x * -1x) = 0
20 + 5x + (3x + -2x2) = 0

Combine like terms: 5x + 3x = 8x
20 + 8x + -2x2 = 0

Solving
20 + 8x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + 4x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(10 + 4x + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + 4x + -1x2 = 0

Solving
10 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-10 + -4x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -4x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -4x + x2 = 0 + 10

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

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

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 = 10 + 4

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

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

Factor a perfect square on the left side:
(x + -2)(x + -2) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -2) equal to 3.741657387 and -3.741657387.


Subproblem 1
x + -2 = 3.741657387

Simplifying
x + -2 = 3.741657387

Reorder the terms:
-2 + x = 3.741657387

Solving
-2 + x = 3.741657387

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 = 3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + x = 3.741657387 + 2
x = 3.741657387 + 2

Combine like terms: 3.741657387 + 2 = 5.741657387
x = 5.741657387

Simplifying
x = 5.741657387


Subproblem 2
x + -2 = -3.741657387

Simplifying
x + -2 = -3.741657387

Reorder the terms:
-2 + x = -3.741657387

Solving
-2 + x = -3.741657387

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 = -3.741657387 + 2

Combine like terms: -2 + 2 = 0
0 + x = -3.741657387 + 2
x = -3.741657387 + 2

Combine like terms: -3.741657387 + 2 = -1.741657387
x = -1.741657387

Simplifying
x = -1.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.741657387, -1.741657387}
Solution
x = {5.741657387, -1.741657387}

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