6x^2+7x-75=0

Solution for 6x^2+7x-75=0 equation:

Simplifying
6x2 + 7x + -75 = 0

Reorder the terms:
-75 + 7x + 6x2 = 0

Solving
-75 + 7x + 6x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-4.166666667, 3}