(3x^2-3x-4)-(2x^2+1)=x^2+8

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Solution for (3x^2-3x-4)-(2x^2+1)=x^2+8 equation: 


Simplifying
(3x2 + -3x + -4) + -1(2x2 + 1) = x2 + 8

Reorder the terms:
(-4 + -3x + 3x2) + -1(2x2 + 1) = x2 + 8

Remove parenthesis around (-4 + -3x + 3x2)
-4 + -3x + 3x2 + -1(2x2 + 1) = x2 + 8

Reorder the terms:
-4 + -3x + 3x2 + -1(1 + 2x2) = x2 + 8
-4 + -3x + 3x2 + (1 * -1 + 2x2 * -1) = x2 + 8
-4 + -3x + 3x2 + (-1 + -2x2) = x2 + 8

Reorder the terms:
-4 + -1 + -3x + 3x2 + -2x2 = x2 + 8

Combine like terms: -4 + -1 = -5
-5 + -3x + 3x2 + -2x2 = x2 + 8

Combine like terms: 3x2 + -2x2 = 1x2
-5 + -3x + 1x2 = x2 + 8

Reorder the terms:
-5 + -3x + 1x2 = 8 + x2

Solving
-5 + -3x + 1x2 = 8 + x2

Solving for variable 'x'.

Reorder the terms:
-5 + -8 + -3x + 1x2 + -1x2 = 8 + x2 + -8 + -1x2

Combine like terms: -5 + -8 = -13
-13 + -3x + 1x2 + -1x2 = 8 + x2 + -8 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-13 + -3x + 0 = 8 + x2 + -8 + -1x2
-13 + -3x = 8 + x2 + -8 + -1x2

Reorder the terms:
-13 + -3x = 8 + -8 + x2 + -1x2

Combine like terms: 8 + -8 = 0
-13 + -3x = 0 + x2 + -1x2
-13 + -3x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-13 + -3x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(13 + 3x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(13 + 3x)' equal to zero and attempt to solve:

Simplifying
13 + 3x = 0

Solving
13 + 3x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 3x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 3x = 0 + -13
3x = 0 + -13

Combine like terms: 0 + -13 = -13
3x = -13

Divide each side by '3'.
x = -4.333333333

Simplifying
x = -4.333333333
Solution
x = {-4.333333333}

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