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

Solution for 4(x^2-1)+(x+1)=0 equation:

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

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

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

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

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

Combine like terms: -4 + 1 = -3
-3 + x + 4x2 = 0

Solving
-3 + x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(3 + -4x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

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

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

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
Solution
x = {-1, 0.75}