126=(x+1)(4x+1)

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Solution for 126=(x+1)(4x+1) equation: 


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

Reorder the terms:
126 = (1 + x)(4x + 1)

Reorder the terms:
126 = (1 + x)(1 + 4x)

Multiply (1 + x) * (1 + 4x)
126 = (1(1 + 4x) + x(1 + 4x))
126 = ((1 * 1 + 4x * 1) + x(1 + 4x))
126 = ((1 + 4x) + x(1 + 4x))
126 = (1 + 4x + (1 * x + 4x * x))
126 = (1 + 4x + (1x + 4x2))

Combine like terms: 4x + 1x = 5x
126 = (1 + 5x + 4x2)

Solving
126 = 1 + 5x + 4x2

Solving for variable 'x'.

Combine like terms: 126 + -1 = 125
125 + -5x + -4x2 = 1 + 5x + 4x2 + -1 + -5x + -4x2

Reorder the terms:
125 + -5x + -4x2 = 1 + -1 + 5x + -5x + 4x2 + -4x2

Combine like terms: 1 + -1 = 0
125 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
125 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
125 + -5x + -4x2 = 0 + 4x2 + -4x2
125 + -5x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
125 + -5x + -4x2 = 0

Factor a trinomial.
(5 + -1x)(25 + 4x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 2
Set the factor '(25 + 4x)' equal to zero and attempt to solve:

Simplifying
25 + 4x = 0

Solving
25 + 4x = 0

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

Add '-25' to each side of the equation.
25 + -25 + 4x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 4x = 0 + -25
4x = 0 + -25

Combine like terms: 0 + -25 = -25
4x = -25

Divide each side by '4'.
x = -6.25

Simplifying
x = -6.25
Solution
x = {5, -6.25}

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