(x+4)(x-9)5x=0

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Solution for (x+4)(x-9)5x=0 equation: 


Simplifying
(x + 4)(x + -9) * 5x = 0

Reorder the terms:
(4 + x)(x + -9) * 5x = 0

Reorder the terms:
(4 + x)(-9 + x) * 5x = 0

Reorder the terms for easier multiplication:
5x(4 + x)(-9 + x) = 0

Multiply (4 + x) * (-9 + x)
5x(4(-9 + x) + x(-9 + x)) = 0
5x((-9 * 4 + x * 4) + x(-9 + x)) = 0
5x((-36 + 4x) + x(-9 + x)) = 0
5x(-36 + 4x + (-9 * x + x * x)) = 0
5x(-36 + 4x + (-9x + x2)) = 0

Combine like terms: 4x + -9x = -5x
5x(-36 + -5x + x2) = 0
(-36 * 5x + -5x * 5x + x2 * 5x) = 0
(-180x + -25x2 + 5x3) = 0

Solving
-180x + -25x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-36 + -5x + x2) = 0

Factor a trinomial.
5x((-4 + -1x)(9 + -1x)) = 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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 3
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {0, -4, 9}

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