9x^2+6x+1=16

Solution for 9x^2+6x+1=16 equation:

Simplifying
9x2 + 6x + 1 = 16

Reorder the terms:
1 + 6x + 9x2 = 16

Solving
1 + 6x + 9x2 = 16

Solving for variable 'x'.

Reorder the terms:
1 + -16 + 6x + 9x2 = 16 + -16

Combine like terms: 1 + -16 = -15
-15 + 6x + 9x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-15 + 6x + 9x2 = 0

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

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

Ignore the factor 3.
Subproblem 1
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
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 = {-1.666666667, 1}