(-9w-8)(-7w+6)=0

Solution for (-9w-8)(-7w+6)=0 equation:

Simplifying
(-9w + -8)(-7w + 6) = 0

Reorder the terms:
(-8 + -9w)(-7w + 6) = 0

Reorder the terms:
(-8 + -9w)(6 + -7w) = 0

Multiply (-8 + -9w) * (6 + -7w)
(-8(6 + -7w) + -9w * (6 + -7w)) = 0
((6 * -8 + -7w * -8) + -9w * (6 + -7w)) = 0
((-48 + 56w) + -9w * (6 + -7w)) = 0
(-48 + 56w + (6 * -9w + -7w * -9w)) = 0
(-48 + 56w + (-54w + 63w2)) = 0

Combine like terms: 56w + -54w = 2w
(-48 + 2w + 63w2) = 0

Solving
-48 + 2w + 63w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-8 + -9w)(6 + -7w) = 0

Subproblem 1
Set the factor '(-8 + -9w)' equal to zero and attempt to solve:

Simplifying
-8 + -9w = 0

Solving
-8 + -9w = 0

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

Add '8' to each side of the equation.
-8 + 8 + -9w = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -9w = 0 + 8
-9w = 0 + 8

Combine like terms: 0 + 8 = 8
-9w = 8

Divide each side by '-9'.
w = -0.8888888889

Simplifying
w = -0.8888888889
Subproblem 2
Set the factor '(6 + -7w)' equal to zero and attempt to solve:

Simplifying
6 + -7w = 0

Solving
6 + -7w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7w = 0 + -6
-7w = 0 + -6

Combine like terms: 0 + -6 = -6
-7w = -6

Divide each side by '-7'.
w = 0.8571428571

Simplifying
w = 0.8571428571
Solution
w = {-0.8888888889, 0.8571428571}