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

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


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

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

Solving
10x + 2x2 = 3x + -1x2

Solving for variable 'x'.

Reorder the terms:
10x + -3x + 2x2 + x2 = 3x + -1x2 + -3x + x2

Combine like terms: 10x + -3x = 7x
7x + 2x2 + x2 = 3x + -1x2 + -3x + x2

Combine like terms: 2x2 + x2 = 3x2
7x + 3x2 = 3x + -1x2 + -3x + x2

Reorder the terms:
7x + 3x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0
7x + 3x2 = 0 + -1x2 + x2
7x + 3x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
7x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 3x) = 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 '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0, -2.333333333}

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