(x+2)(x+5)=180

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Solution for (x+2)(x+5)=180 equation: 


Simplifying
(x + 2)(x + 5) = 180

Reorder the terms:
(2 + x)(x + 5) = 180

Reorder the terms:
(2 + x)(5 + x) = 180

Multiply (2 + x) * (5 + x)
(2(5 + x) + x(5 + x)) = 180
((5 * 2 + x * 2) + x(5 + x)) = 180
((10 + 2x) + x(5 + x)) = 180
(10 + 2x + (5 * x + x * x)) = 180
(10 + 2x + (5x + x2)) = 180

Combine like terms: 2x + 5x = 7x
(10 + 7x + x2) = 180

Solving
10 + 7x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
10 + -180 + 7x + x2 = 180 + -180

Combine like terms: 10 + -180 = -170
-170 + 7x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-170 + 7x + x2 = 0

Factor a trinomial.
(-17 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-17, 10}

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