6x^2-43x+75=0

Solution for 6x^2-43x+75=0 equation:

Simplifying
6x2 + -43x + 75 = 0

Reorder the terms:
75 + -43x + 6x2 = 0

Solving
75 + -43x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(25 + -6x) = 0

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 '(25 + -6x)' equal to zero and attempt to solve:

Simplifying
25 + -6x = 0

Solving
25 + -6x = 0

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

Add '-25' to each side of the equation.
25 + -25 + -6x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -6x = 0 + -25
-6x = 0 + -25

Combine like terms: 0 + -25 = -25
-6x = -25

Divide each side by '-6'.
x = 4.166666667

Simplifying
x = 4.166666667
Solution
x = {3, 4.166666667}