Q(Q+3)=5Q+3

Solution for Q(Q+3)=5Q+3 equation:

Simplifying
Q(Q + 3) = 5Q + 3

Reorder the terms:
Q(3 + Q) = 5Q + 3
(3 * Q + Q * Q) = 5Q + 3
(3Q + Q2) = 5Q + 3

Reorder the terms:
3Q + Q2 = 3 + 5Q

Solving
3Q + Q2 = 3 + 5Q

Solving for variable 'Q'.

Reorder the terms:
-3 + 3Q + -5Q + Q2 = 3 + 5Q + -3 + -5Q

Combine like terms: 3Q + -5Q = -2Q
-3 + -2Q + Q2 = 3 + 5Q + -3 + -5Q

Reorder the terms:
-3 + -2Q + Q2 = 3 + -3 + 5Q + -5Q

Combine like terms: 3 + -3 = 0
-3 + -2Q + Q2 = 0 + 5Q + -5Q
-3 + -2Q + Q2 = 5Q + -5Q

Combine like terms: 5Q + -5Q = 0
-3 + -2Q + Q2 = 0

Factor a trinomial.
(-1 + -1Q)(3 + -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 '(3 + -1Q)' equal to zero and attempt to solve:

Simplifying
3 + -1Q = 0

Solving
3 + -1Q = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1Q = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1Q = 0 + -3
-1Q = 0 + -3

Combine like terms: 0 + -3 = -3
-1Q = -3

Divide each side by '-1'.
Q = 3

Simplifying
Q = 3
Solution
Q = {-1, 3}