85=(x+1)(4x+1)

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Solution for 85=(x+1)(4x+1) equation: 


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

Reorder the terms:
85 = (1 + x)(4x + 1)

Reorder the terms:
85 = (1 + x)(1 + 4x)

Multiply (1 + x) * (1 + 4x)
85 = (1(1 + 4x) + x(1 + 4x))
85 = ((1 * 1 + 4x * 1) + x(1 + 4x))
85 = ((1 + 4x) + x(1 + 4x))
85 = (1 + 4x + (1 * x + 4x * x))
85 = (1 + 4x + (1x + 4x2))

Combine like terms: 4x + 1x = 5x
85 = (1 + 5x + 4x2)

Solving
85 = 1 + 5x + 4x2

Solving for variable 'x'.

Combine like terms: 85 + -1 = 84
84 + -5x + -4x2 = 1 + 5x + 4x2 + -1 + -5x + -4x2

Reorder the terms:
84 + -5x + -4x2 = 1 + -1 + 5x + -5x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
84 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
84 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
84 + -5x + -4x2 = 0 + 4x2 + -4x2
84 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
84 + -5x + -4x2 = 0

Factor a trinomial.
(4 + -1x)(21 + 4x) = 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 '(21 + 4x)' equal to zero and attempt to solve:

Simplifying
21 + 4x = 0

Solving
21 + 4x = 0

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

Add '-21' to each side of the equation.
21 + -21 + 4x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + 4x = 0 + -21
4x = 0 + -21

Combine like terms: 0 + -21 = -21
4x = -21

Divide each side by '4'.
x = -5.25

Simplifying
x = -5.25
Solution
x = {4, -5.25}

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