4q^2-5q-4=2+3q^2

Solution for 4q^2-5q-4=2+3q^2 equation:

Simplifying
4q2 + -5q + -4 = 2 + 3q2

Reorder the terms:
-4 + -5q + 4q2 = 2 + 3q2

Solving
-4 + -5q + 4q2 = 2 + 3q2

Solving for variable 'q'.

Reorder the terms:
-4 + -2 + -5q + 4q2 + -3q2 = 2 + 3q2 + -2 + -3q2

Combine like terms: -4 + -2 = -6
-6 + -5q + 4q2 + -3q2 = 2 + 3q2 + -2 + -3q2

Combine like terms: 4q2 + -3q2 = 1q2
-6 + -5q + 1q2 = 2 + 3q2 + -2 + -3q2

Reorder the terms:
-6 + -5q + 1q2 = 2 + -2 + 3q2 + -3q2

Combine like terms: 2 + -2 = 0
-6 + -5q + 1q2 = 0 + 3q2 + -3q2
-6 + -5q + 1q2 = 3q2 + -3q2

Combine like terms: 3q2 + -3q2 = 0
-6 + -5q + 1q2 = 0

Factor a trinomial.
(-1 + -1q)(6 + -1q) = 0

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

Simplifying
-1 + -1q = 0

Solving
-1 + -1q = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1q = 0 + 1
-1q = 0 + 1

Combine like terms: 0 + 1 = 1
-1q = 1

Divide each side by '-1'.
q = -1

Simplifying
q = -1
Subproblem 2
Set the factor '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6
Solution
q = {-1, 6}