(1[9+w]1)(1[4w-3]1)=0

Solution for (1[9+w]1)(1[4w-3]1)=0 equation:

Simplifying
(1[9 + w] * 1)(1[4w + -3] * 1) = 0

Reorder the terms for easier multiplication:
(1 * 1[9 + w])(1[4w + -3] * 1) = 0

Multiply 1 * 1
(1[9 + w])(1[4w + -3] * 1) = 0
([9 * 1 + w * 1])(1[4w + -3] * 1) = 0
([9 + 1w])(1[4w + -3] * 1) = 0

Reorder the terms:
(9 + 1w)(1[-3 + 4w] * 1) = 0

Reorder the terms for easier multiplication:
(9 + 1w)(1 * 1[-3 + 4w]) = 0

Multiply 1 * 1
(9 + 1w)(1[-3 + 4w]) = 0
(9 + 1w)([-3 * 1 + 4w * 1]) = 0
(9 + 1w)([-3 + 4w]) = 0

Multiply (9 + 1w) * (-3 + 4w)
(9(-3 + 4w) + 1w * (-3 + 4w)) = 0
((-3 * 9 + 4w * 9) + 1w * (-3 + 4w)) = 0
((-27 + 36w) + 1w * (-3 + 4w)) = 0
(-27 + 36w + (-3 * 1w + 4w * 1w)) = 0
(-27 + 36w + (-3w + 4w2)) = 0

Combine like terms: 36w + -3w = 33w
(-27 + 33w + 4w2) = 0

Solving
-27 + 33w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -1w)(3 + -4w) = 0

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

Simplifying
-9 + -1w = 0

Solving
-9 + -1w = 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 + -1w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1w = 0 + 9
-1w = 0 + 9

Combine like terms: 0 + 9 = 9
-1w = 9

Divide each side by '-1'.
w = -9

Simplifying
w = -9
Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve:

Simplifying
3 + -4w = 0

Solving
3 + -4w = 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 + -4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4w = 0 + -3
-4w = 0 + -3

Combine like terms: 0 + -3 = -3
-4w = -3

Divide each side by '-4'.
w = 0.75

Simplifying
w = 0.75
Solution
w = {-9, 0.75}