x+1+3x-3-2(x^2-1)=0

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Solution for x+1+3x-3-2(x^2-1)=0 equation: 


Simplifying
x + 1 + 3x + -3 + -2(x2 + -1) = 0

Reorder the terms:
x + 1 + 3x + -3 + -2(-1 + x2) = 0
x + 1 + 3x + -3 + (-1 * -2 + x2 * -2) = 0
x + 1 + 3x + -3 + (2 + -2x2) = 0

Reorder the terms:
1 + -3 + 2 + x + 3x + -2x2 = 0

Combine like terms: 1 + -3 = -2
-2 + 2 + x + 3x + -2x2 = 0

Combine like terms: -2 + 2 = 0
0 + x + 3x + -2x2 = 0
x + 3x + -2x2 = 0

Combine like terms: x + 3x = 4x
4x + -2x2 = 0

Solving
4x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + -1x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2}

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