6x^2-11x+4=6x+7

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Solution for 6x^2-11x+4=6x+7 equation: 


Simplifying
6x2 + -11x + 4 = 6x + 7

Reorder the terms:
4 + -11x + 6x2 = 6x + 7

Reorder the terms:
4 + -11x + 6x2 = 7 + 6x

Solving
4 + -11x + 6x2 = 7 + 6x

Solving for variable 'x'.

Reorder the terms:
4 + -7 + -11x + -6x + 6x2 = 7 + 6x + -7 + -6x

Combine like terms: 4 + -7 = -3
-3 + -11x + -6x + 6x2 = 7 + 6x + -7 + -6x

Combine like terms: -11x + -6x = -17x
-3 + -17x + 6x2 = 7 + 6x + -7 + -6x

Reorder the terms:
-3 + -17x + 6x2 = 7 + -7 + 6x + -6x

Combine like terms: 7 + -7 = 0
-3 + -17x + 6x2 = 0 + 6x + -6x
-3 + -17x + 6x2 = 6x + -6x

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

Factor a trinomial.
(-1 + -6x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 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 + -6x = 0 + 1

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

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

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667

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 = {-0.1666666667, 3}

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