42x^2=43x-6

Solution for 42x^2=43x-6 equation:

Simplifying
42x2 = 43x + -6

Reorder the terms:
42x2 = -6 + 43x

Solving
42x2 = -6 + 43x

Solving for variable 'x'.

Reorder the terms:
6 + -43x + 42x2 = -6 + 43x + 6 + -43x

Reorder the terms:
6 + -43x + 42x2 = -6 + 6 + 43x + -43x

Combine like terms: -6 + 6 = 0
6 + -43x + 42x2 = 0 + 43x + -43x
6 + -43x + 42x2 = 43x + -43x

Combine like terms: 43x + -43x = 0
6 + -43x + 42x2 = 0

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

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

Simplifying
1 + -6x = 0

Solving
1 + -6x = 0

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

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

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

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

Divide each side by '-6'.
x = 0.1666666667

Simplifying
x = 0.1666666667
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 = {0.1666666667, 0.8571428571}