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

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


Simplifying
(5x + 9)(2x + -1x2) * 5 = 0

Reorder the terms:
(9 + 5x)(2x + -1x2) * 5 = 0

Reorder the terms for easier multiplication:
5(9 + 5x)(2x + -1x2) = 0

Multiply (9 + 5x) * (2x + -1x2)
5(9(2x + -1x2) + 5x * (2x + -1x2)) = 0
5((2x * 9 + -1x2 * 9) + 5x * (2x + -1x2)) = 0
5((18x + -9x2) + 5x * (2x + -1x2)) = 0
5(18x + -9x2 + (2x * 5x + -1x2 * 5x)) = 0
5(18x + -9x2 + (10x2 + -5x3)) = 0

Combine like terms: -9x2 + 10x2 = 1x2
5(18x + 1x2 + -5x3) = 0
(18x * 5 + 1x2 * 5 + -5x3 * 5) = 0
(90x + 5x2 + -25x3) = 0

Solving
90x + 5x2 + -25x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(18 + x + -5x2) = 0

Factor a trinomial.
5x((2 + -1x)(9 + 5x)) = 0

Ignore the factor 5.

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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(9 + 5x)' equal to zero and attempt to solve:

Simplifying
9 + 5x = 0

Solving
9 + 5x = 0

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

Add '-9' to each side of the equation.
9 + -9 + 5x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 5x = 0 + -9
5x = 0 + -9

Combine like terms: 0 + -9 = -9
5x = -9

Divide each side by '5'.
x = -1.8

Simplifying
x = -1.8
Solution
x = {0, 2, -1.8}

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