(2x^2-3x-2)-(x^2+9)=x^2+14

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Solution for (2x^2-3x-2)-(x^2+9)=x^2+14 equation: 


Simplifying
(2x2 + -3x + -2) + -1(x2 + 9) = x2 + 14

Reorder the terms:
(-2 + -3x + 2x2) + -1(x2 + 9) = x2 + 14

Remove parenthesis around (-2 + -3x + 2x2)
-2 + -3x + 2x2 + -1(x2 + 9) = x2 + 14

Reorder the terms:
-2 + -3x + 2x2 + -1(9 + x2) = x2 + 14
-2 + -3x + 2x2 + (9 * -1 + x2 * -1) = x2 + 14
-2 + -3x + 2x2 + (-9 + -1x2) = x2 + 14

Reorder the terms:
-2 + -9 + -3x + 2x2 + -1x2 = x2 + 14

Combine like terms: -2 + -9 = -11
-11 + -3x + 2x2 + -1x2 = x2 + 14

Combine like terms: 2x2 + -1x2 = 1x2
-11 + -3x + 1x2 = x2 + 14

Reorder the terms:
-11 + -3x + 1x2 = 14 + x2

Solving
-11 + -3x + 1x2 = 14 + x2

Solving for variable 'x'.

Reorder the terms:
-11 + -14 + -3x + 1x2 + -1x2 = 14 + x2 + -14 + -1x2

Combine like terms: -11 + -14 = -25
-25 + -3x + 1x2 + -1x2 = 14 + x2 + -14 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-25 + -3x + 0 = 14 + x2 + -14 + -1x2
-25 + -3x = 14 + x2 + -14 + -1x2

Reorder the terms:
-25 + -3x = 14 + -14 + x2 + -1x2

Combine like terms: 14 + -14 = 0
-25 + -3x = 0 + x2 + -1x2
-25 + -3x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-25 + -3x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(25 + 3x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(25 + 3x)' equal to zero and attempt to solve:

Simplifying
25 + 3x = 0

Solving
25 + 3x = 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 + 3x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 3x = 0 + -25
3x = 0 + -25

Combine like terms: 0 + -25 = -25
3x = -25

Divide each side by '3'.
x = -8.333333333

Simplifying
x = -8.333333333
Solution
x = {-8.333333333}

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