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

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


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

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

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

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

Solving for variable 'x'.

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

Combine like terms: 5 + -17 = -12
-12 + -11x + -3x + 6x2 = 17 + 3x + -17 + -3x

Combine like terms: -11x + -3x = -14x
-12 + -14x + 6x2 = 17 + 3x + -17 + -3x

Reorder the terms:
-12 + -14x + 6x2 = 17 + -17 + 3x + -3x

Combine like terms: 17 + -17 = 0
-12 + -14x + 6x2 = 0 + 3x + -3x
-12 + -14x + 6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + -14x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -7x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-0.6666666667, 3}

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