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

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


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

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

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

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

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

Solving
252 = 2 + 5x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
250 + -5x + -2x2 = 2 + -2 + 5x + -5x + 2x2 + -2x2

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

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {10, -12.5}

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