0=-2x^2+20x-42

Solution for 0=-2x^2+20x-42 equation:

Simplifying
0 = -2x2 + 20x + -42

Reorder the terms:
0 = -42 + 20x + -2x2

Solving
0 = -42 + 20x + -2x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + -20x + 2x2 = -42 + 20x + -2x2 + 42 + -20x + 2x2

Reorder the terms:
42 + -20x + 2x2 = -42 + 42 + 20x + -20x + -2x2 + 2x2

Combine like terms: -42 + 42 = 0
42 + -20x + 2x2 = 0 + 20x + -20x + -2x2 + 2x2
42 + -20x + 2x2 = 20x + -20x + -2x2 + 2x2

Combine like terms: 20x + -20x = 0
42 + -20x + 2x2 = 0 + -2x2 + 2x2
42 + -20x + 2x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
42 + -20x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -10x + x2) = 0

Factor a trinomial.
2((3 + -1x)(7 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {3, 7}