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

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


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

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

Reorder the terms:
3x2 + 2x3 + 2x(5x + 3x2) = 0
3x2 + 2x3 + (5x * 2x + 3x2 * 2x) = 0
3x2 + 2x3 + (10x2 + 6x3) = 0

Reorder the terms:
3x2 + 10x2 + 2x3 + 6x3 = 0

Combine like terms: 3x2 + 10x2 = 13x2
13x2 + 2x3 + 6x3 = 0

Combine like terms: 2x3 + 6x3 = 8x3
13x2 + 8x3 = 0

Solving
13x2 + 8x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(13 + 8x) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(13 + 8x)' equal to zero and attempt to solve:

Simplifying
13 + 8x = 0

Solving
13 + 8x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 8x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 8x = 0 + -13
8x = 0 + -13

Combine like terms: 0 + -13 = -13
8x = -13

Divide each side by '8'.
x = -1.625

Simplifying
x = -1.625
Solution
x = {0, -1.625}

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