(-5x+2)*(x+1)+(x+1)=0

Solution for (-5x+2)*(x+1)+(x+1)=0 equation:

Simplifying
(-5x + 2)(x + 1) + (x + 1) = 0

Reorder the terms:
(2 + -5x)(x + 1) + (x + 1) = 0

Reorder the terms:
(2 + -5x)(1 + x) + (x + 1) = 0

Multiply (2 + -5x) * (1 + x)
(2(1 + x) + -5x * (1 + x)) + (x + 1) = 0
((1 * 2 + x * 2) + -5x * (1 + x)) + (x + 1) = 0
((2 + 2x) + -5x * (1 + x)) + (x + 1) = 0
(2 + 2x + (1 * -5x + x * -5x)) + (x + 1) = 0
(2 + 2x + (-5x + -5x2)) + (x + 1) = 0

Combine like terms: 2x + -5x = -3x
(2 + -3x + -5x2) + (x + 1) = 0

Reorder the terms:
2 + -3x + -5x2 + (1 + x) = 0

Remove parenthesis around (1 + x)
2 + -3x + -5x2 + 1 + x = 0

Reorder the terms:
2 + 1 + -3x + x + -5x2 = 0

Combine like terms: 2 + 1 = 3
3 + -3x + x + -5x2 = 0

Combine like terms: -3x + x = -2x
3 + -2x + -5x2 = 0

Solving
3 + -2x + -5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -5x)(1 + x) = 0

Subproblem 1
Set the factor '(3 + -5x)' equal to zero and attempt to solve:

Simplifying
3 + -5x = 0

Solving
3 + -5x = 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 + -5x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5x = 0 + -3
-5x = 0 + -3

Combine like terms: 0 + -3 = -3
-5x = -3

Divide each side by '-5'.
x = 0.6

Simplifying
x = 0.6
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 = {0.6, -1}