(6x^2-11x-1)-(5x^2+6)=x^2+18

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Solution for (6x^2-11x-1)-(5x^2+6)=x^2+18 equation: 


Simplifying
(6x2 + -11x + -1) + -1(5x2 + 6) = x2 + 18

Reorder the terms:
(-1 + -11x + 6x2) + -1(5x2 + 6) = x2 + 18

Remove parenthesis around (-1 + -11x + 6x2)
-1 + -11x + 6x2 + -1(5x2 + 6) = x2 + 18

Reorder the terms:
-1 + -11x + 6x2 + -1(6 + 5x2) = x2 + 18
-1 + -11x + 6x2 + (6 * -1 + 5x2 * -1) = x2 + 18
-1 + -11x + 6x2 + (-6 + -5x2) = x2 + 18

Reorder the terms:
-1 + -6 + -11x + 6x2 + -5x2 = x2 + 18

Combine like terms: -1 + -6 = -7
-7 + -11x + 6x2 + -5x2 = x2 + 18

Combine like terms: 6x2 + -5x2 = 1x2
-7 + -11x + 1x2 = x2 + 18

Reorder the terms:
-7 + -11x + 1x2 = 18 + x2

Solving
-7 + -11x + 1x2 = 18 + x2

Solving for variable 'x'.

Reorder the terms:
-7 + -18 + -11x + 1x2 + -1x2 = 18 + x2 + -18 + -1x2

Combine like terms: -7 + -18 = -25
-25 + -11x + 1x2 + -1x2 = 18 + x2 + -18 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-25 + -11x + 0 = 18 + x2 + -18 + -1x2
-25 + -11x = 18 + x2 + -18 + -1x2

Reorder the terms:
-25 + -11x = 18 + -18 + x2 + -1x2

Combine like terms: 18 + -18 = 0
-25 + -11x = 0 + x2 + -1x2
-25 + -11x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-25 + -11x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 11x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(25 + 11x)' equal to zero and attempt to solve:

Simplifying
25 + 11x = 0

Solving
25 + 11x = 0

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

Add '-25' to each side of the equation.
25 + -25 + 11x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 11x = 0 + -25
11x = 0 + -25

Combine like terms: 0 + -25 = -25
11x = -25

Divide each side by '11'.
x = -2.272727273

Simplifying
x = -2.272727273
Solution
x = {-2.272727273}

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