(-17-2x)(10+3x)=0

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Solution for (-17-2x)(10+3x)=0 equation: 


Simplifying
(-17 + -2x)(10 + 3x) = 0

Multiply (-17 + -2x) * (10 + 3x)
(-17(10 + 3x) + -2x * (10 + 3x)) = 0
((10 * -17 + 3x * -17) + -2x * (10 + 3x)) = 0
((-170 + -51x) + -2x * (10 + 3x)) = 0
(-170 + -51x + (10 * -2x + 3x * -2x)) = 0
(-170 + -51x + (-20x + -6x2)) = 0

Combine like terms: -51x + -20x = -71x
(-170 + -71x + -6x2) = 0

Solving
-170 + -71x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(170 + 71x + 6x2) = 0

Factor a trinomial.
-1((17 + 2x)(10 + 3x)) = 0

Ignore the factor -1.

Subproblem 1
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

Subproblem 2
Set the factor '(10 + 3x)' equal to zero and attempt to solve:

Simplifying
10 + 3x = 0

Solving
10 + 3x = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3x = 0 + -10
3x = 0 + -10

Combine like terms: 0 + -10 = -10
3x = -10

Divide each side by '3'.
x = -3.333333333

Simplifying
x = -3.333333333
Solution
x = {-8.5, -3.333333333}

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