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

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

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

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

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

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

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

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

Add '-2w2' to each side of the equation.
3 + -5w + 2w2 + -2w2 = 1w + 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
3 + -5w + 0 = 1w + 2w2 + -2w2
3 + -5w = 1w + 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
3 + -5w = 1w + 0
3 + -5w = 1w

Solving
3 + -5w = 1w

Solving for variable 'w'.

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

Add '-1w' to each side of the equation.
3 + -5w + -1w = 1w + -1w

Combine like terms: -5w + -1w = -6w
3 + -6w = 1w + -1w

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

Add '-3' to each side of the equation.
3 + -3 + -6w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -6w = 0 + -3
-6w = 0 + -3

Combine like terms: 0 + -3 = -3
-6w = -3

Divide each side by '-6'.
w = 0.5

Simplifying
w = 0.5