42x^2-33x-27=0

Solution for 42x^2-33x-27=0 equation:

Simplifying
42x2 + -33x + -27 = 0

Reorder the terms:
-27 + -33x + 42x2 = 0

Solving
-27 + -33x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -11x + 14x2) = 0

Factor a trinomial.
3((-1 + -2x)(9 + -7x)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(9 + -7x)' equal to zero and attempt to solve:

Simplifying
9 + -7x = 0

Solving
9 + -7x = 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 + -7x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -7x = 0 + -9
-7x = 0 + -9

Combine like terms: 0 + -9 = -9
-7x = -9

Divide each side by '-7'.
x = 1.285714286

Simplifying
x = 1.285714286
Solution
x = {-0.5, 1.285714286}