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

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


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

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

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

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

Combine like terms: -7x + 28x = 21x
(-28 + 21x + 7x2) = 0

Solving
-28 + 21x + 7x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-4 + 3x + x2) = 0

Factor a trinomial.
7((-4 + -1x)(1 + -1x)) = 0

Ignore the factor 7.

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 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Solution
x = {-4, 1}

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