6x(x-1)=35-17x

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Solution for 6x(x-1)=35-17x equation: 


Simplifying
6x(x + -1) = 35 + -17x

Reorder the terms:
6x(-1 + x) = 35 + -17x
(-1 * 6x + x * 6x) = 35 + -17x
(-6x + 6x2) = 35 + -17x

Solving
-6x + 6x2 = 35 + -17x

Solving for variable 'x'.

Reorder the terms:
-35 + -6x + 17x + 6x2 = 35 + -17x + -35 + 17x

Combine like terms: -6x + 17x = 11x
-35 + 11x + 6x2 = 35 + -17x + -35 + 17x

Reorder the terms:
-35 + 11x + 6x2 = 35 + -35 + -17x + 17x

Combine like terms: 35 + -35 = 0
-35 + 11x + 6x2 = 0 + -17x + 17x
-35 + 11x + 6x2 = -17x + 17x

Combine like terms: -17x + 17x = 0
-35 + 11x + 6x2 = 0

Factor a trinomial.
(-7 + -2x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-7 + -2x)' equal to zero and attempt to solve:

Simplifying
-7 + -2x = 0

Solving
-7 + -2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2x = 0 + 7
-2x = 0 + 7

Combine like terms: 0 + 7 = 7
-2x = 7

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-3.5, 1.666666667}

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