66=(x+1)(2x+1)

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Solution for 66=(x+1)(2x+1) equation: 


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

Reorder the terms:
66 = (1 + x)(2x + 1)

Reorder the terms:
66 = (1 + x)(1 + 2x)

Multiply (1 + x) * (1 + 2x)
66 = (1(1 + 2x) + x(1 + 2x))
66 = ((1 * 1 + 2x * 1) + x(1 + 2x))
66 = ((1 + 2x) + x(1 + 2x))
66 = (1 + 2x + (1 * x + 2x * x))
66 = (1 + 2x + (1x + 2x2))

Combine like terms: 2x + 1x = 3x
66 = (1 + 3x + 2x2)

Solving
66 = 1 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 66 + -1 = 65
65 + -3x + -2x2 = 1 + 3x + 2x2 + -1 + -3x + -2x2

Reorder the terms:
65 + -3x + -2x2 = 1 + -1 + 3x + -3x + 2x2 + -2x2

Combine like terms: 1 + -1 = 0
65 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
65 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
65 + -3x + -2x2 = 0 + 2x2 + -2x2
65 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
65 + -3x + -2x2 = 0

Factor a trinomial.
(5 + -1x)(13 + 2x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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 = {5, -6.5}

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