6x^2-4x=10

Solution for 6x^2-4x=10 equation:

Simplifying
6x2 + -4x = 10

Reorder the terms:
-4x + 6x2 = 10

Solving
-4x + 6x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -4x + 6x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -4x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -2x + 3x2) = 0

Factor a trinomial.
2((-1 + -1x)(5 + -3x)) = 0

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

Simplifying
-1 + -1x = 0

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

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {-1, 1.666666667}