6x^2+2x-11=52-45x

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Solution for 6x^2+2x-11=52-45x equation: 


Simplifying
6x2 + 2x + -11 = 52 + -45x

Reorder the terms:
-11 + 2x + 6x2 = 52 + -45x

Solving
-11 + 2x + 6x2 = 52 + -45x

Solving for variable 'x'.

Reorder the terms:
-11 + -52 + 2x + 45x + 6x2 = 52 + -45x + -52 + 45x

Combine like terms: -11 + -52 = -63
-63 + 2x + 45x + 6x2 = 52 + -45x + -52 + 45x

Combine like terms: 2x + 45x = 47x
-63 + 47x + 6x2 = 52 + -45x + -52 + 45x

Reorder the terms:
-63 + 47x + 6x2 = 52 + -52 + -45x + 45x

Combine like terms: 52 + -52 = 0
-63 + 47x + 6x2 = 0 + -45x + 45x
-63 + 47x + 6x2 = -45x + 45x

Combine like terms: -45x + 45x = 0
-63 + 47x + 6x2 = 0

Factor a trinomial.
(-9 + -1x)(7 + -6x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Solution
x = {-9, 1.166666667}

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