144x^2+48x+6=102

Solution for 144x^2+48x+6=102 equation:

Simplifying
144x2 + 48x + 6 = 102

Reorder the terms:
6 + 48x + 144x2 = 102

Solving
6 + 48x + 144x2 = 102

Solving for variable 'x'.

Reorder the terms:
6 + -102 + 48x + 144x2 = 102 + -102

Combine like terms: 6 + -102 = -96
-96 + 48x + 144x2 = 102 + -102

Combine like terms: 102 + -102 = 0
-96 + 48x + 144x2 = 0

Factor out the Greatest Common Factor (GCF), '48'.
48(-2 + x + 3x2) = 0

Factor a trinomial.
48((-1 + -1x)(2 + -3x)) = 0

Ignore the factor 48.
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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1, 0.6666666667}