2w(w+5)=3(w+5)

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

Simplifying
2w(w + 5) = 3(w + 5)

Reorder the terms:
2w(5 + w) = 3(w + 5)
(5 * 2w + w * 2w) = 3(w + 5)
(10w + 2w2) = 3(w + 5)

Reorder the terms:
10w + 2w2 = 3(5 + w)
10w + 2w2 = (5 * 3 + w * 3)
10w + 2w2 = (15 + 3w)

Solving
10w + 2w2 = 15 + 3w

Solving for variable 'w'.

Reorder the terms:
-15 + 10w + -3w + 2w2 = 15 + 3w + -15 + -3w

Combine like terms: 10w + -3w = 7w
-15 + 7w + 2w2 = 15 + 3w + -15 + -3w

Reorder the terms:
-15 + 7w + 2w2 = 15 + -15 + 3w + -3w

Combine like terms: 15 + -15 = 0
-15 + 7w + 2w2 = 0 + 3w + -3w
-15 + 7w + 2w2 = 3w + -3w

Combine like terms: 3w + -3w = 0
-15 + 7w + 2w2 = 0

Factor a trinomial.
(-5 + -1w)(3 + -2w) = 0

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

Simplifying
-5 + -1w = 0

Solving
-5 + -1w = 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 + -1w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1w = 0 + 5
-1w = 0 + 5

Combine like terms: 0 + 5 = 5
-1w = 5

Divide each side by '-1'.
w = -5

Simplifying
w = -5
Subproblem 2
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
Solution
w = {-5, 1.5}