3x^2-9x-5670=0

Solution for 3x^2-9x-5670=0 equation:

Simplifying
3x2 + -9x + -5670 = 0

Reorder the terms:
-5670 + -9x + 3x2 = 0

Solving
-5670 + -9x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1890 + -3x + x2) = 0

Factor a trinomial.
3((-42 + -1x)(45 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-42 + -1x)' equal to zero and attempt to solve:

Simplifying
-42 + -1x = 0

Solving
-42 + -1x = 0

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

Add '42' to each side of the equation.
-42 + 42 + -1x = 0 + 42

Combine like terms: -42 + 42 = 0
0 + -1x = 0 + 42
-1x = 0 + 42

Combine like terms: 0 + 42 = 42
-1x = 42

Divide each side by '-1'.
x = -42

Simplifying
x = -42
Subproblem 2
Set the factor '(45 + -1x)' equal to zero and attempt to solve:

Simplifying
45 + -1x = 0

Solving
45 + -1x = 0

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

Add '-45' to each side of the equation.
45 + -45 + -1x = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -1x = 0 + -45
-1x = 0 + -45

Combine like terms: 0 + -45 = -45
-1x = -45

Divide each side by '-1'.
x = 45

Simplifying
x = 45
Solution
x = {-42, 45}