(7x-7)(8x+1)=0

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Solution for (7x-7)(8x+1)=0 equation: 


Simplifying
(7x + -7)(8x + 1) = 0

Reorder the terms:
(-7 + 7x)(8x + 1) = 0

Reorder the terms:
(-7 + 7x)(1 + 8x) = 0

Multiply (-7 + 7x) * (1 + 8x)
(-7(1 + 8x) + 7x * (1 + 8x)) = 0
((1 * -7 + 8x * -7) + 7x * (1 + 8x)) = 0
((-7 + -56x) + 7x * (1 + 8x)) = 0
(-7 + -56x + (1 * 7x + 8x * 7x)) = 0
(-7 + -56x + (7x + 56x2)) = 0

Combine like terms: -56x + 7x = -49x
(-7 + -49x + 56x2) = 0

Solving
-7 + -49x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-1 + -7x + 8x2) = 0

Factor a trinomial.
7((-1 + -8x)(1 + -1x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-1 + -8x)' equal to zero and attempt to solve:

Simplifying
-1 + -8x = 0

Solving
-1 + -8x = 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 + -8x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x = 0 + 1
-8x = 0 + 1

Combine like terms: 0 + 1 = 1
-8x = 1

Divide each side by '-8'.
x = -0.125

Simplifying
x = -0.125

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 = {-0.125, 1}

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