2w^2+5w+2=-3(2w+1)

Solution for 2w^2+5w+2=-3(2w+1) equation:

Simplifying
2w2 + 5w + 2 = -3(2w + 1)

Reorder the terms:
2 + 5w + 2w2 = -3(2w + 1)

Reorder the terms:
2 + 5w + 2w2 = -3(1 + 2w)
2 + 5w + 2w2 = (1 * -3 + 2w * -3)
2 + 5w + 2w2 = (-3 + -6w)

Solving
2 + 5w + 2w2 = -3 + -6w

Solving for variable 'w'.

Reorder the terms:
2 + 3 + 5w + 6w + 2w2 = -3 + -6w + 3 + 6w

Combine like terms: 2 + 3 = 5
5 + 5w + 6w + 2w2 = -3 + -6w + 3 + 6w

Combine like terms: 5w + 6w = 11w
5 + 11w + 2w2 = -3 + -6w + 3 + 6w

Reorder the terms:
5 + 11w + 2w2 = -3 + 3 + -6w + 6w

Combine like terms: -3 + 3 = 0
5 + 11w + 2w2 = 0 + -6w + 6w
5 + 11w + 2w2 = -6w + 6w

Combine like terms: -6w + 6w = 0
5 + 11w + 2w2 = 0

Factor a trinomial.
(5 + w)(1 + 2w) = 0

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

Simplifying
5 + w = 0

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

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

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

Simplifying
w = -5
Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve:

Simplifying
1 + 2w = 0

Solving
1 + 2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2w = 0 + -1
2w = 0 + -1

Combine like terms: 0 + -1 = -1
2w = -1

Divide each side by '2'.
w = -0.5

Simplifying
w = -0.5
Solution
w = {-5, -0.5}