42a^2-33a-45=

Solution for 42a^2-33a-45= equation:

Simplifying
42a2 + -33a + -45 = 0

Reorder the terms:
-45 + -33a + 42a2 = 0

Solving
-45 + -33a + 42a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -11a + 14a2) = 0

Factor a trinomial.
3((-5 + -7a)(3 + -2a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -7a)' equal to zero and attempt to solve:

Simplifying
-5 + -7a = 0

Solving
-5 + -7a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -7a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7a = 0 + 5
-7a = 0 + 5

Combine like terms: 0 + 5 = 5
-7a = 5

Divide each side by '-7'.
a = -0.7142857143

Simplifying
a = -0.7142857143
Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 0

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

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

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

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

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-0.7142857143, 1.5}