5x^2(2+x)+9(x^3-5x^2)=

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Solution for 5x^2(2+x)+9(x^3-5x^2)= equation: 


Simplifying
5x2(2 + x) + 9(x3 + -5x2) = 0
(2 * 5x2 + x * 5x2) + 9(x3 + -5x2) = 0
(10x2 + 5x3) + 9(x3 + -5x2) = 0

Reorder the terms:
10x2 + 5x3 + 9(-5x2 + x3) = 0
10x2 + 5x3 + (-5x2 * 9 + x3 * 9) = 0
10x2 + 5x3 + (-45x2 + 9x3) = 0

Reorder the terms:
10x2 + -45x2 + 5x3 + 9x3 = 0

Combine like terms: 10x2 + -45x2 = -35x2
-35x2 + 5x3 + 9x3 = 0

Combine like terms: 5x3 + 9x3 = 14x3
-35x2 + 14x3 = 0

Solving
-35x2 + 14x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x2'.
7x2(-5 + 2x) = 0

Ignore the factor 7.

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 '(-5 + 2x)' equal to zero and attempt to solve:

Simplifying
-5 + 2x = 0

Solving
-5 + 2x = 0

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

Add '5' to each side of the equation.
-5 + 5 + 2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2x = 0 + 5
2x = 0 + 5

Combine like terms: 0 + 5 = 5
2x = 5

Divide each side by '2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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