(x+2)(x+1)=420

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Solution for (x+2)(x+1)=420 equation: 


Simplifying
(x + 2)(x + 1) = 420

Reorder the terms:
(2 + x)(x + 1) = 420

Reorder the terms:
(2 + x)(1 + x) = 420

Multiply (2 + x) * (1 + x)
(2(1 + x) + x(1 + x)) = 420
((1 * 2 + x * 2) + x(1 + x)) = 420
((2 + 2x) + x(1 + x)) = 420
(2 + 2x + (1 * x + x * x)) = 420
(2 + 2x + (1x + x2)) = 420

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) = 420

Solving
2 + 3x + x2 = 420

Solving for variable 'x'.

Reorder the terms:
2 + -420 + 3x + x2 = 420 + -420

Combine like terms: 2 + -420 = -418
-418 + 3x + x2 = 420 + -420

Combine like terms: 420 + -420 = 0
-418 + 3x + x2 = 0

Factor a trinomial.
(-22 + -1x)(19 + -1x) = 0


Subproblem 1
Set the factor '(-22 + -1x)' equal to zero and attempt to solve:

Simplifying
-22 + -1x = 0

Solving
-22 + -1x = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x = 0 + 22
-1x = 0 + 22

Combine like terms: 0 + 22 = 22
-1x = 22

Divide each side by '-1'.
x = -22

Simplifying
x = -22

Subproblem 2
Set the factor '(19 + -1x)' equal to zero and attempt to solve:

Simplifying
19 + -1x = 0

Solving
19 + -1x = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1x = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1x = 0 + -19
-1x = 0 + -19

Combine like terms: 0 + -19 = -19
-1x = -19

Divide each side by '-1'.
x = 19

Simplifying
x = 19
Solution
x = {-22, 19}

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