(x+5)(x+5)+3(x+5)=18

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Solution for (x+5)(x+5)+3(x+5)=18 equation: 


Simplifying
(x + 5)(x + 5) + 3(x + 5) = 18

Reorder the terms:
(5 + x)(x + 5) + 3(x + 5) = 18

Reorder the terms:
(5 + x)(5 + x) + 3(x + 5) = 18

Multiply (5 + x) * (5 + x)
(5(5 + x) + x(5 + x)) + 3(x + 5) = 18
((5 * 5 + x * 5) + x(5 + x)) + 3(x + 5) = 18
((25 + 5x) + x(5 + x)) + 3(x + 5) = 18
(25 + 5x + (5 * x + x * x)) + 3(x + 5) = 18
(25 + 5x + (5x + x2)) + 3(x + 5) = 18

Combine like terms: 5x + 5x = 10x
(25 + 10x + x2) + 3(x + 5) = 18

Reorder the terms:
25 + 10x + x2 + 3(5 + x) = 18
25 + 10x + x2 + (5 * 3 + x * 3) = 18
25 + 10x + x2 + (15 + 3x) = 18

Reorder the terms:
25 + 15 + 10x + 3x + x2 = 18

Combine like terms: 25 + 15 = 40
40 + 10x + 3x + x2 = 18

Combine like terms: 10x + 3x = 13x
40 + 13x + x2 = 18

Solving
40 + 13x + x2 = 18

Solving for variable 'x'.

Reorder the terms:
40 + -18 + 13x + x2 = 18 + -18

Combine like terms: 40 + -18 = 22
22 + 13x + x2 = 18 + -18

Combine like terms: 18 + -18 = 0
22 + 13x + x2 = 0

Factor a trinomial.
(11 + x)(2 + x) = 0


Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {-11, -2}

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