(9w-5)(7w-12)=0

Solution for (9w-5)(7w-12)=0 equation:

Simplifying
(9w + -5)(7w + -12) = 0

Reorder the terms:
(-5 + 9w)(7w + -12) = 0

Reorder the terms:
(-5 + 9w)(-12 + 7w) = 0

Multiply (-5 + 9w) * (-12 + 7w)
(-5(-12 + 7w) + 9w * (-12 + 7w)) = 0
((-12 * -5 + 7w * -5) + 9w * (-12 + 7w)) = 0
((60 + -35w) + 9w * (-12 + 7w)) = 0
(60 + -35w + (-12 * 9w + 7w * 9w)) = 0
(60 + -35w + (-108w + 63w2)) = 0

Combine like terms: -35w + -108w = -143w
(60 + -143w + 63w2) = 0

Solving
60 + -143w + 63w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(5 + -9w)(12 + -7w) = 0

Subproblem 1
Set the factor '(5 + -9w)' equal to zero and attempt to solve:

Simplifying
5 + -9w = 0

Solving
5 + -9w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -9w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9w = 0 + -5
-9w = 0 + -5

Combine like terms: 0 + -5 = -5
-9w = -5

Divide each side by '-9'.
w = 0.5555555556

Simplifying
w = 0.5555555556
Subproblem 2
Set the factor '(12 + -7w)' equal to zero and attempt to solve:

Simplifying
12 + -7w = 0

Solving
12 + -7w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -7w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -7w = 0 + -12
-7w = 0 + -12

Combine like terms: 0 + -12 = -12
-7w = -12

Divide each side by '-7'.
w = 1.714285714

Simplifying
w = 1.714285714
Solution
w = {0.5555555556, 1.714285714}