3(-4x^2+16x+9)=0

Solution for 3(-4x^2+16x+9)=0 equation:

Simplifying
3(-4x2 + 16x + 9) = 0

Reorder the terms:
3(9 + 16x + -4x2) = 0
(9 * 3 + 16x * 3 + -4x2 * 3) = 0
(27 + 48x + -12x2) = 0

Solving
27 + 48x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + 16x + -4x2) = 0

Factor a trinomial.
3((9 + -2x)(1 + 2x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + -2x)' equal to zero and attempt to solve:

Simplifying
9 + -2x = 0

Solving
9 + -2x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2x = 0 + -9
-2x = 0 + -9

Combine like terms: 0 + -9 = -9
-2x = -9

Divide each side by '-2'.
x = 4.5

Simplifying
x = 4.5
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {4.5, -0.5}