(3x^2-7x-3)-(2x^2+1)=x^2+11

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Solution for (3x^2-7x-3)-(2x^2+1)=x^2+11 equation: 


Simplifying
(3x2 + -7x + -3) + -1(2x2 + 1) = x2 + 11

Reorder the terms:
(-3 + -7x + 3x2) + -1(2x2 + 1) = x2 + 11

Remove parenthesis around (-3 + -7x + 3x2)
-3 + -7x + 3x2 + -1(2x2 + 1) = x2 + 11

Reorder the terms:
-3 + -7x + 3x2 + -1(1 + 2x2) = x2 + 11
-3 + -7x + 3x2 + (1 * -1 + 2x2 * -1) = x2 + 11
-3 + -7x + 3x2 + (-1 + -2x2) = x2 + 11

Reorder the terms:
-3 + -1 + -7x + 3x2 + -2x2 = x2 + 11

Combine like terms: -3 + -1 = -4
-4 + -7x + 3x2 + -2x2 = x2 + 11

Combine like terms: 3x2 + -2x2 = 1x2
-4 + -7x + 1x2 = x2 + 11

Reorder the terms:
-4 + -7x + 1x2 = 11 + x2

Solving
-4 + -7x + 1x2 = 11 + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -11 + -7x + 1x2 + -1x2 = 11 + x2 + -11 + -1x2

Combine like terms: -4 + -11 = -15
-15 + -7x + 1x2 + -1x2 = 11 + x2 + -11 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-15 + -7x + 0 = 11 + x2 + -11 + -1x2
-15 + -7x = 11 + x2 + -11 + -1x2

Reorder the terms:
-15 + -7x = 11 + -11 + x2 + -1x2

Combine like terms: 11 + -11 = 0
-15 + -7x = 0 + x2 + -1x2
-15 + -7x = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-15 + -7x = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 7x) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(15 + 7x)' equal to zero and attempt to solve:

Simplifying
15 + 7x = 0

Solving
15 + 7x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 7x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 7x = 0 + -15
7x = 0 + -15

Combine like terms: 0 + -15 = -15
7x = -15

Divide each side by '7'.
x = -2.142857143

Simplifying
x = -2.142857143
Solution
x = {-2.142857143}

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