(2x+1)(x+2)=54

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Solution for (2x+1)(x+2)=54 equation: 


Simplifying
(2x + 1)(x + 2) = 54

Reorder the terms:
(1 + 2x)(x + 2) = 54

Reorder the terms:
(1 + 2x)(2 + x) = 54

Multiply (1 + 2x) * (2 + x)
(1(2 + x) + 2x * (2 + x)) = 54
((2 * 1 + x * 1) + 2x * (2 + x)) = 54
((2 + 1x) + 2x * (2 + x)) = 54
(2 + 1x + (2 * 2x + x * 2x)) = 54
(2 + 1x + (4x + 2x2)) = 54

Combine like terms: 1x + 4x = 5x
(2 + 5x + 2x2) = 54

Solving
2 + 5x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
2 + -54 + 5x + 2x2 = 54 + -54

Combine like terms: 2 + -54 = -52
-52 + 5x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-52 + 5x + 2x2 = 0

Factor a trinomial.
(-13 + -2x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve:

Simplifying
-13 + -2x = 0

Solving
-13 + -2x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2x = 0 + 13
-2x = 0 + 13

Combine like terms: 0 + 13 = 13
-2x = 13

Divide each side by '-2'.
x = -6.5

Simplifying
x = -6.5

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-6.5, 4}

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