0=42x^2-13x-42

Solution for 0=42x^2-13x-42 equation:

Simplifying
0 = 42x2 + -13x + -42

Reorder the terms:
0 = -42 + -13x + 42x2

Solving
0 = -42 + -13x + 42x2

Solving for variable 'x'.

Combine like terms: 0 + 42 = 42
42 + 13x + -42x2 = -42 + -13x + 42x2 + 42 + 13x + -42x2

Reorder the terms:
42 + 13x + -42x2 = -42 + 42 + -13x + 13x + 42x2 + -42x2

Combine like terms: -42 + 42 = 0
42 + 13x + -42x2 = 0 + -13x + 13x + 42x2 + -42x2
42 + 13x + -42x2 = -13x + 13x + 42x2 + -42x2

Combine like terms: -13x + 13x = 0
42 + 13x + -42x2 = 0 + 42x2 + -42x2
42 + 13x + -42x2 = 42x2 + -42x2

Combine like terms: 42x2 + -42x2 = 0
42 + 13x + -42x2 = 0

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

Subproblem 1
Set the factor '(7 + -6x)' equal to zero and attempt to solve:

Simplifying
7 + -6x = 0

Solving
7 + -6x = 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 + -6x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6x = 0 + -7
-6x = 0 + -7

Combine like terms: 0 + -7 = -7
-6x = -7

Divide each side by '-6'.
x = 1.166666667

Simplifying
x = 1.166666667
Subproblem 2
Set the factor '(6 + 7x)' equal to zero and attempt to solve:

Simplifying
6 + 7x = 0

Solving
6 + 7x = 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 + 7x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7x = 0 + -6
7x = 0 + -6

Combine like terms: 0 + -6 = -6
7x = -6

Divide each side by '7'.
x = -0.8571428571

Simplifying
x = -0.8571428571
Solution
x = {1.166666667, -0.8571428571}