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

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


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

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

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

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

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

Solving
54 = 2 + 5x + 2x2

Solving for variable 'x'.

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

Reorder the terms:
52 + -5x + -2x2 = 2 + -2 + 5x + -5x + 2x2 + -2x2

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

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {4, -6.5}

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