4(x^2-55x+106)=0

Solution for 4(x^2-55x+106)=0 equation:

Simplifying
4(x2 + -55x + 106) = 0

Reorder the terms:
4(106 + -55x + x2) = 0
(106 * 4 + -55x * 4 + x2 * 4) = 0
(424 + -220x + 4x2) = 0

Solving
424 + -220x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(106 + -55x + x2) = 0

Factor a trinomial.
4((2 + -1x)(53 + -1x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(53 + -1x)' equal to zero and attempt to solve:

Simplifying
53 + -1x = 0

Solving
53 + -1x = 0

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

Add '-53' to each side of the equation.
53 + -53 + -1x = 0 + -53

Combine like terms: 53 + -53 = 0
0 + -1x = 0 + -53
-1x = 0 + -53

Combine like terms: 0 + -53 = -53
-1x = -53

Divide each side by '-1'.
x = 53

Simplifying
x = 53
Solution
x = {2, 53}