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

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


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

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

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

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

Combine like terms: 1x + 4x = 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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