175=(x+1)(4x+1)

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Solution for 175=(x+1)(4x+1) equation: 


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

Reorder the terms:
175 = (1 + x)(4x + 1)

Reorder the terms:
175 = (1 + x)(1 + 4x)

Multiply (1 + x) * (1 + 4x)
175 = (1(1 + 4x) + x(1 + 4x))
175 = ((1 * 1 + 4x * 1) + x(1 + 4x))
175 = ((1 + 4x) + x(1 + 4x))
175 = (1 + 4x + (1 * x + 4x * x))
175 = (1 + 4x + (1x + 4x2))

Combine like terms: 4x + 1x = 5x
175 = (1 + 5x + 4x2)

Solving
175 = 1 + 5x + 4x2

Solving for variable 'x'.

Combine like terms: 175 + -1 = 174
174 + -5x + -4x2 = 1 + 5x + 4x2 + -1 + -5x + -4x2

Reorder the terms:
174 + -5x + -4x2 = 1 + -1 + 5x + -5x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
174 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
174 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
174 + -5x + -4x2 = 0 + 4x2 + -4x2
174 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
174 + -5x + -4x2 = 0

Factor a trinomial.
(6 + -1x)(29 + 4x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(29 + 4x)' equal to zero and attempt to solve:

Simplifying
29 + 4x = 0

Solving
29 + 4x = 0

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

Add '-29' to each side of the equation.
29 + -29 + 4x = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 4x = 0 + -29
4x = 0 + -29

Combine like terms: 0 + -29 = -29
4x = -29

Divide each side by '4'.
x = -7.25

Simplifying
x = -7.25
Solution
x = {6, -7.25}

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