(5w+8)(2w+1)=-2w-4

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Solution for (5w+8)(2w+1)=-2w-4 equation: 


Simplifying
(5w + 8)(2w + 1) = -2w + -4

Reorder the terms:
(8 + 5w)(2w + 1) = -2w + -4

Reorder the terms:
(8 + 5w)(1 + 2w) = -2w + -4

Multiply (8 + 5w) * (1 + 2w)
(8(1 + 2w) + 5w * (1 + 2w)) = -2w + -4
((1 * 8 + 2w * 8) + 5w * (1 + 2w)) = -2w + -4
((8 + 16w) + 5w * (1 + 2w)) = -2w + -4
(8 + 16w + (1 * 5w + 2w * 5w)) = -2w + -4
(8 + 16w + (5w + 10w2)) = -2w + -4

Combine like terms: 16w + 5w = 21w
(8 + 21w + 10w2) = -2w + -4

Reorder the terms:
8 + 21w + 10w2 = -4 + -2w

Solving
8 + 21w + 10w2 = -4 + -2w

Solving for variable 'w'.

Reorder the terms:
8 + 4 + 21w + 2w + 10w2 = -4 + -2w + 4 + 2w

Combine like terms: 8 + 4 = 12
12 + 21w + 2w + 10w2 = -4 + -2w + 4 + 2w

Combine like terms: 21w + 2w = 23w
12 + 23w + 10w2 = -4 + -2w + 4 + 2w

Reorder the terms:
12 + 23w + 10w2 = -4 + 4 + -2w + 2w

Combine like terms: -4 + 4 = 0
12 + 23w + 10w2 = 0 + -2w + 2w
12 + 23w + 10w2 = -2w + 2w

Combine like terms: -2w + 2w = 0
12 + 23w + 10w2 = 0

Factor a trinomial.
(3 + 2w)(4 + 5w) = 0


Subproblem 1
Set the factor '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5

Subproblem 2
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
Solution
w = {-1.5, -0.8}

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