45=(4x+1)(x+1)

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Solution for 45=(4x+1)(x+1) equation: 


Simplifying
45 = (4x + 1)(x + 1)

Reorder the terms:
45 = (1 + 4x)(x + 1)

Reorder the terms:
45 = (1 + 4x)(1 + x)

Multiply (1 + 4x) * (1 + x)
45 = (1(1 + x) + 4x * (1 + x))
45 = ((1 * 1 + x * 1) + 4x * (1 + x))
45 = ((1 + 1x) + 4x * (1 + x))
45 = (1 + 1x + (1 * 4x + x * 4x))
45 = (1 + 1x + (4x + 4x2))

Combine like terms: 1x + 4x = 5x
45 = (1 + 5x + 4x2)

Solving
45 = 1 + 5x + 4x2

Solving for variable 'x'.

Combine like terms: 45 + -1 = 44
44 + -5x + -4x2 = 1 + 5x + 4x2 + -1 + -5x + -4x2

Reorder the terms:
44 + -5x + -4x2 = 1 + -1 + 5x + -5x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
44 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
44 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
44 + -5x + -4x2 = 0 + 4x2 + -4x2
44 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
44 + -5x + -4x2 = 0

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


Subproblem 1
Set the factor '(11 + -4x)' equal to zero and attempt to solve:

Simplifying
11 + -4x = 0

Solving
11 + -4x = 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 + -4x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -4x = 0 + -11
-4x = 0 + -11

Combine like terms: 0 + -11 = -11
-4x = -11

Divide each side by '-4'.
x = 2.75

Simplifying
x = 2.75

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

Simplifying
4 + x = 0

Solving
4 + x = 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 + x = 0 + -4

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

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

Simplifying
x = -4
Solution
x = {2.75, -4}

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