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

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

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

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

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

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

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

Solving
-3 + -1w + 2w2 = 3

Solving for variable 'w'.

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

Combine like terms: -3 + -3 = -6
-6 + -1w + 2w2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + -1w + 2w2 = 0

Factor a trinomial.
(-3 + -2w)(2 + -1w) = 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 '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

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

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

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

Divide each side by '-1'.
w = 2

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