(5w+3)(4w+6)=11w+6

Solution for (5w+3)(4w+6)=11w+6 equation:

Simplifying
(5w + 3)(4w + 6) = 11w + 6

Reorder the terms:
(3 + 5w)(4w + 6) = 11w + 6

Reorder the terms:
(3 + 5w)(6 + 4w) = 11w + 6

Multiply (3 + 5w) * (6 + 4w)
(3(6 + 4w) + 5w * (6 + 4w)) = 11w + 6
((6 * 3 + 4w * 3) + 5w * (6 + 4w)) = 11w + 6
((18 + 12w) + 5w * (6 + 4w)) = 11w + 6
(18 + 12w + (6 * 5w + 4w * 5w)) = 11w + 6
(18 + 12w + (30w + 20w2)) = 11w + 6

Combine like terms: 12w + 30w = 42w
(18 + 42w + 20w2) = 11w + 6

Reorder the terms:
18 + 42w + 20w2 = 6 + 11w

Solving
18 + 42w + 20w2 = 6 + 11w

Solving for variable 'w'.

Reorder the terms:
18 + -6 + 42w + -11w + 20w2 = 6 + 11w + -6 + -11w

Combine like terms: 18 + -6 = 12
12 + 42w + -11w + 20w2 = 6 + 11w + -6 + -11w

Combine like terms: 42w + -11w = 31w
12 + 31w + 20w2 = 6 + 11w + -6 + -11w

Reorder the terms:
12 + 31w + 20w2 = 6 + -6 + 11w + -11w

Combine like terms: 6 + -6 = 0
12 + 31w + 20w2 = 0 + 11w + -11w
12 + 31w + 20w2 = 11w + -11w

Combine like terms: 11w + -11w = 0
12 + 31w + 20w2 = 0

Factor a trinomial.
(4 + 5w)(3 + 4w) = 0

Subproblem 1
Set the factor '(4 + 5w)' equal to zero and attempt to solve:

Simplifying
4 + 5w = 0

Solving
4 + 5w = 0

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

Add '-4' to each side of the equation.
4 + -4 + 5w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5w = 0 + -4
5w = 0 + -4

Combine like terms: 0 + -4 = -4
5w = -4

Divide each side by '5'.
w = -0.8

Simplifying
w = -0.8
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 = {-0.8, -0.75}