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

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


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

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

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

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

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

Solving
1 + 5x + 4x2 = 175

Solving for variable 'x'.

Reorder the terms:
1 + -175 + 5x + 4x2 = 175 + -175

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

Combine like terms: 175 + -175 = 0
-174 + 5x + 4x2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-7.25, 6}

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