0=2x^2-5x-42

Solution for 0=2x^2-5x-42 equation:

Simplifying
0 = 2x2 + -5x + -42

Reorder the terms:
0 = -42 + -5x + 2x2

Solving
0 = -42 + -5x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + 5x + -2x2 = -42 + -5x + 2x2 + 42 + 5x + -2x2

Reorder the terms:
42 + 5x + -2x2 = -42 + 42 + -5x + 5x + 2x2 + -2x2

Combine like terms: -42 + 42 = 0
42 + 5x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2
42 + 5x + -2x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
42 + 5x + -2x2 = 0 + 2x2 + -2x2
42 + 5x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
42 + 5x + -2x2 = 0

Factor a trinomial.
(6 + -1x)(7 + 2x) = 0

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 '(7 + 2x)' equal to zero and attempt to solve:

Simplifying
7 + 2x = 0

Solving
7 + 2x = 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 + 2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2x = 0 + -7
2x = 0 + -7

Combine like terms: 0 + -7 = -7
2x = -7

Divide each side by '2'.
x = -3.5

Simplifying
x = -3.5
Solution
x = {6, -3.5}