6x(x-1)=10-17x

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Solution for 6x(x-1)=10-17x equation: 


Simplifying
6x(x + -1) = 10 + -17x

Reorder the terms:
6x(-1 + x) = 10 + -17x
(-1 * 6x + x * 6x) = 10 + -17x
(-6x + 6x2) = 10 + -17x

Solving
-6x + 6x2 = 10 + -17x

Solving for variable 'x'.

Reorder the terms:
-10 + -6x + 17x + 6x2 = 10 + -17x + -10 + 17x

Combine like terms: -6x + 17x = 11x
-10 + 11x + 6x2 = 10 + -17x + -10 + 17x

Reorder the terms:
-10 + 11x + 6x2 = 10 + -10 + -17x + 17x

Combine like terms: 10 + -10 = 0
-10 + 11x + 6x2 = 0 + -17x + 17x
-10 + 11x + 6x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
-10 + 11x + 6x2 = 0

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


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-2.5, 0.6666666667}

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