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

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

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

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

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

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

Combine like terms: -48w + 9w = -39w
(-54 + -39w + 8w2) = 0

Solving
-54 + -39w + 8w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -8w)(6 + -1w) = 0

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

Simplifying
-9 + -8w = 0

Solving
-9 + -8w = 0

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

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

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

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

Divide each side by '-8'.
w = -1.125

Simplifying
w = -1.125
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 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 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {-1.125, 6}