12x^2-17x-4=1

Solution for 12x^2-17x-4=1 equation:

Simplifying
12x2 + -17x + -4 = 1

Reorder the terms:
-4 + -17x + 12x2 = 1

Solving
-4 + -17x + 12x2 = 1

Solving for variable 'x'.

Reorder the terms:
-4 + -1 + -17x + 12x2 = 1 + -1

Combine like terms: -4 + -1 = -5
-5 + -17x + 12x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-5 + -17x + 12x2 = 0

Factor a trinomial.
(-1 + -4x)(5 + -3x) = 0

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

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

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

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25
Subproblem 2
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
Solution
x = {-0.25, 1.666666667}