(-10x+5)(-11x+17)=0

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Solution for (-10x+5)(-11x+17)=0 equation: 


Simplifying
(-10x + 5)(-11x + 17) = 0

Reorder the terms:
(5 + -10x)(-11x + 17) = 0

Reorder the terms:
(5 + -10x)(17 + -11x) = 0

Multiply (5 + -10x) * (17 + -11x)
(5(17 + -11x) + -10x * (17 + -11x)) = 0
((17 * 5 + -11x * 5) + -10x * (17 + -11x)) = 0
((85 + -55x) + -10x * (17 + -11x)) = 0
(85 + -55x + (17 * -10x + -11x * -10x)) = 0
(85 + -55x + (-170x + 110x2)) = 0

Combine like terms: -55x + -170x = -225x
(85 + -225x + 110x2) = 0

Solving
85 + -225x + 110x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(17 + -45x + 22x2) = 0

Factor a trinomial.
5((1 + -2x)(17 + -11x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(17 + -11x)' equal to zero and attempt to solve:

Simplifying
17 + -11x = 0

Solving
17 + -11x = 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 + -11x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -11x = 0 + -17
-11x = 0 + -17

Combine like terms: 0 + -17 = -17
-11x = -17

Divide each side by '-11'.
x = 1.545454545

Simplifying
x = 1.545454545
Solution
x = {0.5, 1.545454545}

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