234=2x^2+20x+42

Solution for 234=2x^2+20x+42 equation:

Simplifying
234 = 2x2 + 20x + 42

Reorder the terms:
234 = 42 + 20x + 2x2

Solving
234 = 42 + 20x + 2x2

Solving for variable 'x'.

Combine like terms: 234 + -42 = 192
192 + -20x + -2x2 = 42 + 20x + 2x2 + -42 + -20x + -2x2

Reorder the terms:
192 + -20x + -2x2 = 42 + -42 + 20x + -20x + 2x2 + -2x2

Combine like terms: 42 + -42 = 0
192 + -20x + -2x2 = 0 + 20x + -20x + 2x2 + -2x2
192 + -20x + -2x2 = 20x + -20x + 2x2 + -2x2

Combine like terms: 20x + -20x = 0
192 + -20x + -2x2 = 0 + 2x2 + -2x2
192 + -20x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
192 + -20x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(96 + -10x + -1x2) = 0

Factor a trinomial.
2((6 + -1x)(16 + x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Solution
x = {6, -16}