(8w+3)(5w-6)=0

Solution for (8w+3)(5w-6)=0 equation:

Simplifying
(8w + 3)(5w + -6) = 0

Reorder the terms:
(3 + 8w)(5w + -6) = 0

Reorder the terms:
(3 + 8w)(-6 + 5w) = 0

Multiply (3 + 8w) * (-6 + 5w)
(3(-6 + 5w) + 8w * (-6 + 5w)) = 0
((-6 * 3 + 5w * 3) + 8w * (-6 + 5w)) = 0
((-18 + 15w) + 8w * (-6 + 5w)) = 0
(-18 + 15w + (-6 * 8w + 5w * 8w)) = 0
(-18 + 15w + (-48w + 40w2)) = 0

Combine like terms: 15w + -48w = -33w
(-18 + -33w + 40w2) = 0

Solving
-18 + -33w + 40w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -8w)(6 + -5w) = 0

Subproblem 1
Set the factor '(-3 + -8w)' equal to zero and attempt to solve:

Simplifying
-3 + -8w = 0

Solving
-3 + -8w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -8w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -8w = 0 + 3
-8w = 0 + 3

Combine like terms: 0 + 3 = 3
-8w = 3

Divide each side by '-8'.
w = -0.375

Simplifying
w = -0.375
Subproblem 2
Set the factor '(6 + -5w)' equal to zero and attempt to solve:

Simplifying
6 + -5w = 0

Solving
6 + -5w = 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 + -5w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5w = 0 + -6
-5w = 0 + -6

Combine like terms: 0 + -6 = -6
-5w = -6

Divide each side by '-5'.
w = 1.2

Simplifying
w = 1.2
Solution
w = {-0.375, 1.2}