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

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


Simplifying
(4x + 1)(x2 + -1) + -1(2x2 + x + -1)(2x) = 0

Reorder the terms:
(1 + 4x)(x2 + -1) + -1(2x2 + x + -1)(2x) = 0

Reorder the terms:
(1 + 4x)(-1 + x2) + -1(2x2 + x + -1)(2x) = 0

Multiply (1 + 4x) * (-1 + x2)
(1(-1 + x2) + 4x * (-1 + x2)) + -1(2x2 + x + -1)(2x) = 0
((-1 * 1 + x2 * 1) + 4x * (-1 + x2)) + -1(2x2 + x + -1)(2x) = 0
((-1 + 1x2) + 4x * (-1 + x2)) + -1(2x2 + x + -1)(2x) = 0
(-1 + 1x2 + (-1 * 4x + x2 * 4x)) + -1(2x2 + x + -1)(2x) = 0
(-1 + 1x2 + (-4x + 4x3)) + -1(2x2 + x + -1)(2x) = 0

Reorder the terms:
(-1 + -4x + 1x2 + 4x3) + -1(2x2 + x + -1)(2x) = 0
(-1 + -4x + 1x2 + 4x3) + -1(2x2 + x + -1)(2x) = 0

Reorder the terms:
-1 + -4x + 1x2 + 4x3 + -1(-1 + x + 2x2)(2x) = 0

Remove parenthesis around (2x)
-1 + -4x + 1x2 + 4x3 + -1(-1 + x + 2x2) * 2x = 0

Reorder the terms for easier multiplication:
-1 + -4x + 1x2 + 4x3 + -1 * 2x(-1 + x + 2x2) = 0

Multiply -1 * 2
-1 + -4x + 1x2 + 4x3 + -2x(-1 + x + 2x2) = 0
-1 + -4x + 1x2 + 4x3 + (-1 * -2x + x * -2x + 2x2 * -2x) = 0
-1 + -4x + 1x2 + 4x3 + (2x + -2x2 + -4x3) = 0

Reorder the terms:
-1 + -4x + 2x + 1x2 + -2x2 + 4x3 + -4x3 = 0

Combine like terms: -4x + 2x = -2x
-1 + -2x + 1x2 + -2x2 + 4x3 + -4x3 = 0

Combine like terms: 1x2 + -2x2 = -1x2
-1 + -2x + -1x2 + 4x3 + -4x3 = 0

Combine like terms: 4x3 + -4x3 = 0
-1 + -2x + -1x2 + 0 = 0
-1 + -2x + -1x2 = 0

Solving
-1 + -2x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2x + x2) = 0

Factor a trinomial.
-1((1 + x)(1 + x)) = 0

Ignore the factor -1.

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1

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

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {-1, -1}

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