(x+2)(x)=675

Solution for (x+2)(x)=675 equation:

Simplifying
(x + 2)(x) = 675

Reorder the terms:
(2 + x)(x) = 675

Reorder the terms for easier multiplication:
x(2 + x) = 675
(2 * x + x * x) = 675
(2x + x2) = 675

Solving
2x + x2 = 675

Solving for variable 'x'.

Reorder the terms:
-675 + 2x + x2 = 675 + -675

Combine like terms: 675 + -675 = 0
-675 + 2x + x2 = 0

Factor a trinomial.
(-27 + -1x)(25 + -1x) = 0

Subproblem 1
Set the factor '(-27 + -1x)' equal to zero and attempt to solve:

Simplifying
-27 + -1x = 0

Solving
-27 + -1x = 0

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

Add '27' to each side of the equation.
-27 + 27 + -1x = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x = 0 + 27
-1x = 0 + 27

Combine like terms: 0 + 27 = 27
-1x = 27

Divide each side by '-1'.
x = -27

Simplifying
x = -27
Subproblem 2
Set the factor '(25 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

Simplifying
x = 25
Solution
x = {-27, 25}