(2w-7)(w)=30

Solution for (2w-7)(w)=30 equation:

Simplifying
(2w + -7)(w) = 30

Reorder the terms:
(-7 + 2w)(w) = 30

Reorder the terms for easier multiplication:
w(-7 + 2w) = 30
(-7 * w + 2w * w) = 30
(-7w + 2w2) = 30

Solving
-7w + 2w2 = 30

Solving for variable 'w'.

Reorder the terms:
-30 + -7w + 2w2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -7w + 2w2 = 0

Factor a trinomial.
(-5 + -2w)(6 + -1w) = 0

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

Simplifying
-5 + -2w = 0

Solving
-5 + -2w = 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 + -2w = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2w = 0 + 5
-2w = 0 + 5

Combine like terms: 0 + 5 = 5
-2w = 5

Divide each side by '-2'.
w = -2.5

Simplifying
w = -2.5
Subproblem 2
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

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

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

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Solution
w = {-2.5, 6}