45=(x+1)(2x+1)

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Solution for 45=(x+1)(2x+1) equation: 


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

Reorder the terms:
45 = (1 + x)(2x + 1)

Reorder the terms:
45 = (1 + x)(1 + 2x)

Multiply (1 + x) * (1 + 2x)
45 = (1(1 + 2x) + x(1 + 2x))
45 = ((1 * 1 + 2x * 1) + x(1 + 2x))
45 = ((1 + 2x) + x(1 + 2x))
45 = (1 + 2x + (1 * x + 2x * x))
45 = (1 + 2x + (1x + 2x2))

Combine like terms: 2x + 1x = 3x
45 = (1 + 3x + 2x2)

Solving
45 = 1 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 45 + -1 = 44
44 + -3x + -2x2 = 1 + 3x + 2x2 + -1 + -3x + -2x2

Reorder the terms:
44 + -3x + -2x2 = 1 + -1 + 3x + -3x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
44 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
44 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
44 + -3x + -2x2 = 0 + 2x2 + -2x2
44 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
44 + -3x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(11 + 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 '(11 + 2x)' equal to zero and attempt to solve:

Simplifying
11 + 2x = 0

Solving
11 + 2x = 0

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

Add '-11' to each side of the equation.
11 + -11 + 2x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + 2x = 0 + -11
2x = 0 + -11

Combine like terms: 0 + -11 = -11
2x = -11

Divide each side by '2'.
x = -5.5

Simplifying
x = -5.5
Solution
x = {4, -5.5}

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