0=-16x^2+46x+6

Solution for 0=-16x^2+46x+6 equation:

Simplifying
0 = -16x2 + 46x + 6

Reorder the terms:
0 = 6 + 46x + -16x2

Solving
0 = 6 + 46x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -46x + 16x2 = 6 + 46x + -16x2 + -6 + -46x + 16x2

Reorder the terms:
-6 + -46x + 16x2 = 6 + -6 + 46x + -46x + -16x2 + 16x2

Combine like terms: 6 + -6 = 0
-6 + -46x + 16x2 = 0 + 46x + -46x + -16x2 + 16x2
-6 + -46x + 16x2 = 46x + -46x + -16x2 + 16x2

Combine like terms: 46x + -46x = 0
-6 + -46x + 16x2 = 0 + -16x2 + 16x2
-6 + -46x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-6 + -46x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -23x + 8x2) = 0

Factor a trinomial.
2((-1 + -8x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -8x)' equal to zero and attempt to solve:

Simplifying
-1 + -8x = 0

Solving
-1 + -8x = 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 + -8x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -8x = 0 + 1
-8x = 0 + 1

Combine like terms: 0 + 1 = 1
-8x = 1

Divide each side by '-8'.
x = -0.125

Simplifying
x = -0.125
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 = {-0.125, 3}