414=(x+5-2)(x-2)(1)

Solution for 414=(x+5-2)(x-2)(1) equation:

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

Reorder the terms:
414 = (5 + -2 + x)(x + -2)(1)

Combine like terms: 5 + -2 = 3
414 = (3 + x)(x + -2)(1)

Reorder the terms:
414 = (3 + x)(-2 + x)(1)

Reorder the terms for easier multiplication:
414 = 1(3 + x)(-2 + x)

Multiply (3 + x) * (-2 + x)
414 = 1(3(-2 + x) + x(-2 + x))
414 = 1((-2 * 3 + x * 3) + x(-2 + x))
414 = 1((-6 + 3x) + x(-2 + x))
414 = 1(-6 + 3x + (-2 * x + x * x))
414 = 1(-6 + 3x + (-2x + x2))

Combine like terms: 3x + -2x = 1x
414 = 1(-6 + 1x + x2)
414 = (-6 * 1 + 1x * 1 + x2 * 1)
414 = (-6 + 1x + 1x2)

Solving
414 = -6 + 1x + 1x2

Solving for variable 'x'.

Combine like terms: 414 + 6 = 420
420 + -1x + -1x2 = -6 + 1x + 1x2 + 6 + -1x + -1x2

Reorder the terms:
420 + -1x + -1x2 = -6 + 6 + 1x + -1x + 1x2 + -1x2

Combine like terms: -6 + 6 = 0
420 + -1x + -1x2 = 0 + 1x + -1x + 1x2 + -1x2
420 + -1x + -1x2 = 1x + -1x + 1x2 + -1x2

Combine like terms: 1x + -1x = 0
420 + -1x + -1x2 = 0 + 1x2 + -1x2
420 + -1x + -1x2 = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
420 + -1x + -1x2 = 0

Factor a trinomial.
(20 + -1x)(21 + x) = 0

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(21 + x)' equal to zero and attempt to solve:

Simplifying
21 + x = 0

Solving
21 + x = 0

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

Add '-21' to each side of the equation.
21 + -21 + x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + x = 0 + -21
x = 0 + -21

Combine like terms: 0 + -21 = -21
x = -21

Simplifying
x = -21
Solution
x = {20, -21}