1=7w-10w^2

Solution for 1=7w-10w^2 equation:

Simplifying
1 = 7w + -10w2

Solving
1 = 7w + -10w2

Solving for variable 'w'.

Reorder the terms:
1 + -7w + 10w2 = 7w + -7w + -10w2 + 10w2

Combine like terms: 7w + -7w = 0
1 + -7w + 10w2 = 0 + -10w2 + 10w2
1 + -7w + 10w2 = -10w2 + 10w2

Combine like terms: -10w2 + 10w2 = 0
1 + -7w + 10w2 = 0

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

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

Simplifying
1 + -5w = 0

Solving
1 + -5w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -5w = 0 + -1

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

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

Divide each side by '-5'.
w = 0.2

Simplifying
w = 0.2
Subproblem 2
Set the factor '(1 + -2w)' equal to zero and attempt to solve:

Simplifying
1 + -2w = 0

Solving
1 + -2w = 0

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

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

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

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

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Solution
w = {0.2, 0.5}