0=12-17x+6x^2

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Solution for 0=12-17x+6x^2 equation: 


Simplifying
0 = 12 + -17x + 6x2

Solving
0 = 12 + -17x + 6x2

Solving for variable 'x'.

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

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

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

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

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

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


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

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 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 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
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
Solution
x = {1.5, 1.333333333}

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