(9x^3-45x^2)(-x+5)=0

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Solution for (9x^3-45x^2)(-x+5)=0 equation: 


Simplifying
(9x3 + -45x2)(-1x + 5) = 0

Reorder the terms:
(-45x2 + 9x3)(-1x + 5) = 0

Reorder the terms:
(-45x2 + 9x3)(5 + -1x) = 0

Multiply (-45x2 + 9x3) * (5 + -1x)
(-45x2 * (5 + -1x) + 9x3 * (5 + -1x)) = 0
((5 * -45x2 + -1x * -45x2) + 9x3 * (5 + -1x)) = 0
((-225x2 + 45x3) + 9x3 * (5 + -1x)) = 0
(-225x2 + 45x3 + (5 * 9x3 + -1x * 9x3)) = 0
(-225x2 + 45x3 + (45x3 + -9x4)) = 0

Combine like terms: 45x3 + 45x3 = 90x3
(-225x2 + 90x3 + -9x4) = 0

Solving
-225x2 + 90x3 + -9x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x2'.
9x2(-25 + 10x + -1x2) = 0

Factor a trinomial.
9x2((-5 + x)(5 + -1x)) = 0

Ignore the factor 9.

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 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 5, 5}

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