6x^2-58x=20

Solution for 6x^2-58x=20 equation:

Simplifying
6x2 + -58x = 20

Reorder the terms:
-58x + 6x2 = 20

Solving
-58x + 6x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -58x + 6x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -58x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -29x + 3x2) = 0

Factor a trinomial.
2((-1 + -3x)(10 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-0.3333333333, 10}