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

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


Simplifying
2x(x + 5) + -1x2(3 + -1x) = 0

Reorder the terms:
2x(5 + x) + -1x2(3 + -1x) = 0
(5 * 2x + x * 2x) + -1x2(3 + -1x) = 0
(10x + 2x2) + -1x2(3 + -1x) = 0
10x + 2x2 + (3 * -1x2 + -1x * -1x2) = 0
10x + 2x2 + (-3x2 + 1x3) = 0

Combine like terms: 2x2 + -3x2 = -1x2
10x + -1x2 + 1x3 = 0

Solving
10x + -1x2 + 1x3 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
10 + -1x + x2 = 0

Solving
10 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -1x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -1x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x + x2 = 0 + -10
-1x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1x + x2 = -10

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -10 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -10 + 0.25

Combine like terms: -10 + 0.25 = -9.75
0.25 + -1x + x2 = -9.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -9.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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