0=-8x^2+2x+6

Solution for 0=-8x^2+2x+6 equation:

Simplifying
0 = -8x2 + 2x + 6

Reorder the terms:
0 = 6 + 2x + -8x2

Solving
0 = 6 + 2x + -8x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -2x + 8x2 = 6 + 2x + -8x2 + -6 + -2x + 8x2

Reorder the terms:
-6 + -2x + 8x2 = 6 + -6 + 2x + -2x + -8x2 + 8x2

Combine like terms: 6 + -6 = 0
-6 + -2x + 8x2 = 0 + 2x + -2x + -8x2 + 8x2
-6 + -2x + 8x2 = 2x + -2x + -8x2 + 8x2

Combine like terms: 2x + -2x = 0
-6 + -2x + 8x2 = 0 + -8x2 + 8x2
-6 + -2x + 8x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-6 + -2x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -1x + 4x2) = 0

Factor a trinomial.
2((-3 + -4x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
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
Solution
x = {-0.75, 1}