6x^2-17x+11=-5+3x

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Solution for 6x^2-17x+11=-5+3x equation:


Simplifying
6x2 + -17x + 11 = -5 + 3x

Reorder the terms:
11 + -17x + 6x2 = -5 + 3x

Solving
11 + -17x + 6x2 = -5 + 3x

Solving for variable 'x'.

Reorder the terms:
11 + 5 + -17x + -3x + 6x2 = -5 + 3x + 5 + -3x

Combine like terms: 11 + 5 = 16
16 + -17x + -3x + 6x2 = -5 + 3x + 5 + -3x

Combine like terms: -17x + -3x = -20x
16 + -20x + 6x2 = -5 + 3x + 5 + -3x

Reorder the terms:
16 + -20x + 6x2 = -5 + 5 + 3x + -3x

Combine like terms: -5 + 5 = 0
16 + -20x + 6x2 = 0 + 3x + -3x
16 + -20x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
16 + -20x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -10x + 3x2) = 0

Factor a trinomial.
2((4 + -3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.333333333, 2}

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