4(x-17)x(x+5)=0

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Solution for 4(x-17)x(x+5)=0 equation: 


Simplifying
4(x + -17) * x(x + 5) = 0

Reorder the terms:
4(-17 + x) * x(x + 5) = 0

Reorder the terms:
4(-17 + x) * x(5 + x) = 0

Reorder the terms for easier multiplication:
4x(-17 + x)(5 + x) = 0

Multiply (-17 + x) * (5 + x)
4x(-17(5 + x) + x(5 + x)) = 0
4x((5 * -17 + x * -17) + x(5 + x)) = 0
4x((-85 + -17x) + x(5 + x)) = 0
4x(-85 + -17x + (5 * x + x * x)) = 0
4x(-85 + -17x + (5x + x2)) = 0

Combine like terms: -17x + 5x = -12x
4x(-85 + -12x + x2) = 0
(-85 * 4x + -12x * 4x + x2 * 4x) = 0
(-340x + -48x2 + 4x3) = 0

Solving
-340x + -48x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-85 + -12x + x2) = 0

Factor a trinomial.
4x((-5 + -1x)(17 + -1x)) = 0

Ignore the factor 4.

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 + -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

Subproblem 3
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 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 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {0, -5, 17}

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