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

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

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

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

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

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

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

Solving
1 + 3x + 2x2 = 45

Solving for variable 'x'.

Reorder the terms:
1 + -45 + 3x + 2x2 = 45 + -45

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

Combine like terms: 45 + -45 = 0
-44 + 3x + 2x2 = 0

Factor a trinomial.
(-11 + -2x)(4 + -1x) = 0

Subproblem 1
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
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 = {-5.5, 4}