q(q+4)+4=6q+3

Solution for q(q+4)+4=6q+3 equation:

Simplifying
q(q + 4) + 4 = 6q + 3

Reorder the terms:
q(4 + q) + 4 = 6q + 3
(4 * q + q * q) + 4 = 6q + 3
(4q + q2) + 4 = 6q + 3

Reorder the terms:
4 + 4q + q2 = 6q + 3

Reorder the terms:
4 + 4q + q2 = 3 + 6q

Solving
4 + 4q + q2 = 3 + 6q

Solving for variable 'q'.

Reorder the terms:
4 + -3 + 4q + -6q + q2 = 3 + 6q + -3 + -6q

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

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

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

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

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

Factor a trinomial.
(1 + -1q)(1 + -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 '(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
Solution
q = {1, 1}