4w^2-52w+48=

Solution for 4w^2-52w+48= equation:

Simplifying
4w2 + -52w + 48 = 0

Reorder the terms:
48 + -52w + 4w2 = 0

Solving
48 + -52w + 4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + -13w + w2) = 0

Factor a trinomial.
4((1 + -1w)(12 + -1w)) = 0

Ignore the factor 4.
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 '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1w = 0 + -12
-1w = 0 + -12

Combine like terms: 0 + -12 = -12
-1w = -12

Divide each side by '-1'.
w = 12

Simplifying
w = 12
Solution
w = {1, 12}