(w+2)(3w-1)=10

Solution for (w+2)(3w-1)=10 equation:

Simplifying
(w + 2)(3w + -1) = 10

Reorder the terms:
(2 + w)(3w + -1) = 10

Reorder the terms:
(2 + w)(-1 + 3w) = 10

Multiply (2 + w) * (-1 + 3w)
(2(-1 + 3w) + w(-1 + 3w)) = 10
((-1 * 2 + 3w * 2) + w(-1 + 3w)) = 10
((-2 + 6w) + w(-1 + 3w)) = 10
(-2 + 6w + (-1 * w + 3w * w)) = 10
(-2 + 6w + (-1w + 3w2)) = 10

Combine like terms: 6w + -1w = 5w
(-2 + 5w + 3w2) = 10

Solving
-2 + 5w + 3w2 = 10

Solving for variable 'w'.

Reorder the terms:
-2 + -10 + 5w + 3w2 = 10 + -10

Combine like terms: -2 + -10 = -12
-12 + 5w + 3w2 = 10 + -10

Combine like terms: 10 + -10 = 0
-12 + 5w + 3w2 = 0

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

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

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 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 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

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

Simplifying
4 + -3w = 0

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

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

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

Divide each side by '-3'.
w = 1.333333333

Simplifying
w = 1.333333333
Solution
w = {-3, 1.333333333}