-42x^2-53x-15=0

Solution for -42x^2-53x-15=0 equation:

Simplifying
-42x2 + -53x + -15 = 0

Reorder the terms:
-15 + -53x + -42x2 = 0

Solving
-15 + -53x + -42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 53x + 42x2) = 0

Factor a trinomial.
-1((5 + 6x)(3 + 7x)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 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 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Subproblem 2
Set the factor '(3 + 7x)' equal to zero and attempt to solve:

Simplifying
3 + 7x = 0

Solving
3 + 7x = 0

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

Add '-3' to each side of the equation.
3 + -3 + 7x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7x = 0 + -3
7x = 0 + -3

Combine like terms: 0 + -3 = -3
7x = -3

Divide each side by '7'.
x = -0.4285714286

Simplifying
x = -0.4285714286
Solution
x = {-0.8333333333, -0.4285714286}