(7x-1)(1x+4)=0

Solution for (7x-1)(1x+4)=0 equation:

Simplifying
(7x + -1)(1x + 4) = 0

Reorder the terms:
(-1 + 7x)(1x + 4) = 0

Reorder the terms:
(-1 + 7x)(4 + 1x) = 0

Multiply (-1 + 7x) * (4 + 1x)
(-1(4 + 1x) + 7x * (4 + 1x)) = 0
((4 * -1 + 1x * -1) + 7x * (4 + 1x)) = 0
((-4 + -1x) + 7x * (4 + 1x)) = 0
(-4 + -1x + (4 * 7x + 1x * 7x)) = 0
(-4 + -1x + (28x + 7x2)) = 0

Combine like terms: -1x + 28x = 27x
(-4 + 27x + 7x2) = 0

Solving
-4 + 27x + 7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -1x)(1 + -7x) = 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 '(1 + -7x)' equal to zero and attempt to solve:

Simplifying
1 + -7x = 0

Solving
1 + -7x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -7x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7x = 0 + -1
-7x = 0 + -1

Combine like terms: 0 + -1 = -1
-7x = -1

Divide each side by '-7'.
x = 0.1428571429

Simplifying
x = 0.1428571429
Solution
x = {-4, 0.1428571429}