6x(x-3)=17x^2-19x

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Solution for 6x(x-3)=17x^2-19x equation: 


Simplifying
6x(x + -3) = 17x2 + -19x

Reorder the terms:
6x(-3 + x) = 17x2 + -19x
(-3 * 6x + x * 6x) = 17x2 + -19x
(-18x + 6x2) = 17x2 + -19x

Reorder the terms:
-18x + 6x2 = -19x + 17x2

Solving
-18x + 6x2 = -19x + 17x2

Solving for variable 'x'.

Reorder the terms:
-18x + 19x + 6x2 + -17x2 = -19x + 17x2 + 19x + -17x2

Combine like terms: -18x + 19x = 1x
1x + 6x2 + -17x2 = -19x + 17x2 + 19x + -17x2

Combine like terms: 6x2 + -17x2 = -11x2
1x + -11x2 = -19x + 17x2 + 19x + -17x2

Reorder the terms:
1x + -11x2 = -19x + 19x + 17x2 + -17x2

Combine like terms: -19x + 19x = 0
1x + -11x2 = 0 + 17x2 + -17x2
1x + -11x2 = 17x2 + -17x2

Combine like terms: 17x2 + -17x2 = 0
1x + -11x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + -11x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + -11x)' equal to zero and attempt to solve:

Simplifying
1 + -11x = 0

Solving
1 + -11x = 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 + -11x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -11x = 0 + -1
-11x = 0 + -1

Combine like terms: 0 + -1 = -1
-11x = -1

Divide each side by '-11'.
x = 0.09090909091

Simplifying
x = 0.09090909091
Solution
x = {0, 0.09090909091}

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