338=-16x^2+48x+402

Solution for 338=-16x^2+48x+402 equation:

Simplifying
338 = -16x2 + 48x + 402

Reorder the terms:
338 = 402 + 48x + -16x2

Solving
338 = 402 + 48x + -16x2

Solving for variable 'x'.

Combine like terms: 338 + -402 = -64
-64 + -48x + 16x2 = 402 + 48x + -16x2 + -402 + -48x + 16x2

Reorder the terms:
-64 + -48x + 16x2 = 402 + -402 + 48x + -48x + -16x2 + 16x2

Combine like terms: 402 + -402 = 0
-64 + -48x + 16x2 = 0 + 48x + -48x + -16x2 + 16x2
-64 + -48x + 16x2 = 48x + -48x + -16x2 + 16x2

Combine like terms: 48x + -48x = 0
-64 + -48x + 16x2 = 0 + -16x2 + 16x2
-64 + -48x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-64 + -48x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-4 + -3x + x2) = 0

Factor a trinomial.
16((-1 + -1x)(4 + -1x)) = 0

Ignore the factor 16.
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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-1, 4}