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

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

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

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

Combine like terms: x + 7x = 8x
-1x(-8 + 8x) = 0
(-8 * -1x + 8x * -1x) = 0
(8x + -8x2) = 0

Solving
8x + -8x2 = 0

Solving for variable 'x'.

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

Ignore the factor 8.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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, 1}