0=2(2x^2-103x+546)

Solution for 0=2(2x^2-103x+546) equation:

Simplifying
0 = 2(2x2 + -103x + 546)

Reorder the terms:
0 = 2(546 + -103x + 2x2)
0 = (546 * 2 + -103x * 2 + 2x2 * 2)
0 = (1092 + -206x + 4x2)

Solving
0 = 1092 + -206x + 4x2

Solving for variable 'x'.

Combine like terms: 0 + -1092 = -1092
-1092 + 206x + -4x2 = 1092 + -206x + 4x2 + -1092 + 206x + -4x2

Reorder the terms:
-1092 + 206x + -4x2 = 1092 + -1092 + -206x + 206x + 4x2 + -4x2

Combine like terms: 1092 + -1092 = 0
-1092 + 206x + -4x2 = 0 + -206x + 206x + 4x2 + -4x2
-1092 + 206x + -4x2 = -206x + 206x + 4x2 + -4x2

Combine like terms: -206x + 206x = 0
-1092 + 206x + -4x2 = 0 + 4x2 + -4x2
-1092 + 206x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-1092 + 206x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-546 + 103x + -2x2) = 0

Factor a trinomial.
2((-91 + 2x)(6 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-91 + 2x)' equal to zero and attempt to solve:

Simplifying
-91 + 2x = 0

Solving
-91 + 2x = 0

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

Add '91' to each side of the equation.
-91 + 91 + 2x = 0 + 91

Combine like terms: -91 + 91 = 0
0 + 2x = 0 + 91
2x = 0 + 91

Combine like terms: 0 + 91 = 91
2x = 91

Divide each side by '2'.
x = 45.5

Simplifying
x = 45.5
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {45.5, 6}