0=3x^2-17x+10

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Solution for 0=3x^2-17x+10 equation: 


Simplifying
0 = 3x2 + -17x + 10

Reorder the terms:
0 = 10 + -17x + 3x2

Solving
0 = 10 + -17x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -10 = -10
-10 + 17x + -3x2 = 10 + -17x + 3x2 + -10 + 17x + -3x2

Reorder the terms:
-10 + 17x + -3x2 = 10 + -10 + -17x + 17x + 3x2 + -3x2

Combine like terms: 10 + -10 = 0
-10 + 17x + -3x2 = 0 + -17x + 17x + 3x2 + -3x2
-10 + 17x + -3x2 = -17x + 17x + 3x2 + -3x2

Combine like terms: -17x + 17x = 0
-10 + 17x + -3x2 = 0 + 3x2 + -3x2
-10 + 17x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-10 + 17x + -3x2 = 0

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


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

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

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

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

Simplifying
x = 5

Subproblem 2
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
Solution
x = {5, 0.6666666667}

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