(x+1)(x+1)-5(x+1)+6=0

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Solution for (x+1)(x+1)-5(x+1)+6=0 equation: 


Simplifying
(x + 1)(x + 1) + -5(x + 1) + 6 = 0

Reorder the terms:
(1 + x)(x + 1) + -5(x + 1) + 6 = 0

Reorder the terms:
(1 + x)(1 + x) + -5(x + 1) + 6 = 0

Multiply (1 + x) * (1 + x)
(1(1 + x) + x(1 + x)) + -5(x + 1) + 6 = 0
((1 * 1 + x * 1) + x(1 + x)) + -5(x + 1) + 6 = 0
((1 + 1x) + x(1 + x)) + -5(x + 1) + 6 = 0
(1 + 1x + (1 * x + x * x)) + -5(x + 1) + 6 = 0
(1 + 1x + (1x + x2)) + -5(x + 1) + 6 = 0

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + -5(x + 1) + 6 = 0

Reorder the terms:
1 + 2x + x2 + -5(1 + x) + 6 = 0
1 + 2x + x2 + (1 * -5 + x * -5) + 6 = 0
1 + 2x + x2 + (-5 + -5x) + 6 = 0

Reorder the terms:
1 + -5 + 6 + 2x + -5x + x2 = 0

Combine like terms: 1 + -5 = -4
-4 + 6 + 2x + -5x + x2 = 0

Combine like terms: -4 + 6 = 2
2 + 2x + -5x + x2 = 0

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

Solving
2 + -3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(2 + -1x) = 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 '(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 = {1, 2}

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