6x^2-20x-17=9

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Solution for 6x^2-20x-17=9 equation:


Simplifying
6x2 + -20x + -17 = 9

Reorder the terms:
-17 + -20x + 6x2 = 9

Solving
-17 + -20x + 6x2 = 9

Solving for variable 'x'.

Reorder the terms:
-17 + -9 + -20x + 6x2 = 9 + -9

Combine like terms: -17 + -9 = -26
-26 + -20x + 6x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-26 + -20x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + -10x + 3x2) = 0

Factor a trinomial.
2((-1 + -1x)(13 + -3x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 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 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1

Subproblem 2

Set the factor '(13 + -3x)' equal to zero and attempt to solve: Simplifying 13 + -3x = 0 Solving 13 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -3x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -3x = 0 + -13 -3x = 0 + -13 Combine like terms: 0 + -13 = -13 -3x = -13 Divide each side by '-3'. x = 4.333333333 Simplifying x = 4.333333333

Solution

x = {-1, 4.333333333}

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