6(w-3)(w-3)+1=25

Solution for 6(w-3)(w-3)+1=25 equation:

Simplifying
6(w + -3)(w + -3) + 1 = 25

Reorder the terms:
6(-3 + w)(w + -3) + 1 = 25

Reorder the terms:
6(-3 + w)(-3 + w) + 1 = 25

Multiply (-3 + w) * (-3 + w)
6(-3(-3 + w) + w(-3 + w)) + 1 = 25
6((-3 * -3 + w * -3) + w(-3 + w)) + 1 = 25
6((9 + -3w) + w(-3 + w)) + 1 = 25
6(9 + -3w + (-3 * w + w * w)) + 1 = 25
6(9 + -3w + (-3w + w2)) + 1 = 25

Combine like terms: -3w + -3w = -6w
6(9 + -6w + w2) + 1 = 25
(9 * 6 + -6w * 6 + w2 * 6) + 1 = 25
(54 + -36w + 6w2) + 1 = 25

Reorder the terms:
54 + 1 + -36w + 6w2 = 25

Combine like terms: 54 + 1 = 55
55 + -36w + 6w2 = 25

Solving
55 + -36w + 6w2 = 25

Solving for variable 'w'.

Reorder the terms:
55 + -25 + -36w + 6w2 = 25 + -25

Combine like terms: 55 + -25 = 30
30 + -36w + 6w2 = 25 + -25

Combine like terms: 25 + -25 = 0
30 + -36w + 6w2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(5 + -6w + w2) = 0

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

Ignore the factor 6.
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 '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 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 + -1w = 0 + -5

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

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

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {1, 5}