=6x^2-5x+1

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Solution for =6x^2-5x+1 equation: 


Simplifying
0 = 6x2 + -5x + 1

Reorder the terms:
0 = 1 + -5x + 6x2

Solving
0 = 1 + -5x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + 5x + -6x2 = 1 + -5x + 6x2 + -1 + 5x + -6x2

Reorder the terms:
-1 + 5x + -6x2 = 1 + -1 + -5x + 5x + 6x2 + -6x2

Combine like terms: 1 + -1 = 0
-1 + 5x + -6x2 = 0 + -5x + 5x + 6x2 + -6x2
-1 + 5x + -6x2 = -5x + 5x + 6x2 + -6x2

Combine like terms: -5x + 5x = 0
-1 + 5x + -6x2 = 0 + 6x2 + -6x2
-1 + 5x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-1 + 5x + -6x2 = 0

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


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

Simplifying
-1 + 2x = 0

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

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

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

Divide each side by '2'.
x = 0.5

Simplifying
x = 0.5

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 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 + -3x = 0 + -1

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

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

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0.5, 0.3333333333}

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