6w^2+1=2w+5w^2

Solution for 6w^2+1=2w+5w^2 equation:

Simplifying
6w2 + 1 = 2w + 5w2

Reorder the terms:
1 + 6w2 = 2w + 5w2

Solving
1 + 6w2 = 2w + 5w2

Solving for variable 'w'.

Reorder the terms:
1 + -2w + 6w2 + -5w2 = 2w + 5w2 + -2w + -5w2

Combine like terms: 6w2 + -5w2 = 1w2
1 + -2w + 1w2 = 2w + 5w2 + -2w + -5w2

Reorder the terms:
1 + -2w + 1w2 = 2w + -2w + 5w2 + -5w2

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

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

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

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

Simplifying
1 + -1w = 0

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

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

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

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

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

Simplifying
1 + -1w = 0

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

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

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

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

Simplifying
w = 1
Solution
w = {1, 1}