0=6x^2-47x+77

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Solution for 0=6x^2-47x+77 equation: 


Simplifying
0 = 6x2 + -47x + 77

Reorder the terms:
0 = 77 + -47x + 6x2

Solving
0 = 77 + -47x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -77 = -77
-77 + 47x + -6x2 = 77 + -47x + 6x2 + -77 + 47x + -6x2

Reorder the terms:
-77 + 47x + -6x2 = 77 + -77 + -47x + 47x + 6x2 + -6x2

Combine like terms: 77 + -77 = 0
-77 + 47x + -6x2 = 0 + -47x + 47x + 6x2 + -6x2
-77 + 47x + -6x2 = -47x + 47x + 6x2 + -6x2

Combine like terms: -47x + 47x = 0
-77 + 47x + -6x2 = 0 + 6x2 + -6x2
-77 + 47x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-77 + 47x + -6x2 = 0

Factor a trinomial.
(-11 + 2x)(7 + -3x) = 0


Subproblem 1
Set the factor '(-11 + 2x)' equal to zero and attempt to solve:

Simplifying
-11 + 2x = 0

Solving
-11 + 2x = 0

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

Add '11' to each side of the equation.
-11 + 11 + 2x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 2x = 0 + 11
2x = 0 + 11

Combine like terms: 0 + 11 = 11
2x = 11

Divide each side by '2'.
x = 5.5

Simplifying
x = 5.5

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {5.5, 2.333333333}

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