(x+2)(2x+1)=252

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Solution for (x+2)(2x+1)=252 equation: 


Simplifying
(x + 2)(2x + 1) = 252

Reorder the terms:
(2 + x)(2x + 1) = 252

Reorder the terms:
(2 + x)(1 + 2x) = 252

Multiply (2 + x) * (1 + 2x)
(2(1 + 2x) + x(1 + 2x)) = 252
((1 * 2 + 2x * 2) + x(1 + 2x)) = 252
((2 + 4x) + x(1 + 2x)) = 252
(2 + 4x + (1 * x + 2x * x)) = 252
(2 + 4x + (1x + 2x2)) = 252

Combine like terms: 4x + 1x = 5x
(2 + 5x + 2x2) = 252

Solving
2 + 5x + 2x2 = 252

Solving for variable 'x'.

Reorder the terms:
2 + -252 + 5x + 2x2 = 252 + -252

Combine like terms: 2 + -252 = -250
-250 + 5x + 2x2 = 252 + -252

Combine like terms: 252 + -252 = 0
-250 + 5x + 2x2 = 0

Factor a trinomial.
(-25 + -2x)(10 + -1x) = 0


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

Simplifying
-25 + -2x = 0

Solving
-25 + -2x = 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 + -2x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -2x = 0 + 25
-2x = 0 + 25

Combine like terms: 0 + 25 = 25
-2x = 25

Divide each side by '-2'.
x = -12.5

Simplifying
x = -12.5

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 = {-12.5, 10}

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