17(x+2)(x-5)=0

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Solution for 17(x+2)(x-5)=0 equation: 


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

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

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

Multiply (2 + x) * (-5 + x)
17(2(-5 + x) + x(-5 + x)) = 0
17((-5 * 2 + x * 2) + x(-5 + x)) = 0
17((-10 + 2x) + x(-5 + x)) = 0
17(-10 + 2x + (-5 * x + x * x)) = 0
17(-10 + 2x + (-5x + x2)) = 0

Combine like terms: 2x + -5x = -3x
17(-10 + -3x + x2) = 0
(-10 * 17 + -3x * 17 + x2 * 17) = 0
(-170 + -51x + 17x2) = 0

Solving
-170 + -51x + 17x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '17'.
17(-10 + -3x + x2) = 0

Factor a trinomial.
17((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 17.

Subproblem 1
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 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
Solution
x = {-2, 5}

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