(2x-17)(3x+5)x=

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Solution for (2x-17)(3x+5)x= equation: 


Simplifying
(2x + -17)(3x + 5) * x = 0

Reorder the terms:
(-17 + 2x)(3x + 5) * x = 0

Reorder the terms:
(-17 + 2x)(5 + 3x) * x = 0

Reorder the terms for easier multiplication:
x(-17 + 2x)(5 + 3x) = 0

Multiply (-17 + 2x) * (5 + 3x)
x(-17(5 + 3x) + 2x * (5 + 3x)) = 0
x((5 * -17 + 3x * -17) + 2x * (5 + 3x)) = 0
x((-85 + -51x) + 2x * (5 + 3x)) = 0
x(-85 + -51x + (5 * 2x + 3x * 2x)) = 0
x(-85 + -51x + (10x + 6x2)) = 0

Combine like terms: -51x + 10x = -41x
x(-85 + -41x + 6x2) = 0
(-85 * x + -41x * x + 6x2 * x) = 0
(-85x + -41x2 + 6x3) = 0

Solving
-85x + -41x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-85 + -41x + 6x2) = 0

Factor a trinomial.
x((-5 + -3x)(17 + -2x)) = 0


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 '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 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 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 3
Set the factor '(17 + -2x)' equal to zero and attempt to solve:

Simplifying
17 + -2x = 0

Solving
17 + -2x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -2x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -2x = 0 + -17
-2x = 0 + -17

Combine like terms: 0 + -17 = -17
-2x = -17

Divide each side by '-2'.
x = 8.5

Simplifying
x = 8.5
Solution
x = {0, -1.666666667, 8.5}

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