5+3q(q-4)=(q+1)

Solution for 5+3q(q-4)=(q+1) equation:

Simplifying
5 + 3q(q + -4) = (q + 1)

Reorder the terms:
5 + 3q(-4 + q) = (q + 1)
5 + (-4 * 3q + q * 3q) = (q + 1)
5 + (-12q + 3q2) = (q + 1)

Reorder the terms:
5 + -12q + 3q2 = (1 + q)

Remove parenthesis around (1 + q)
5 + -12q + 3q2 = 1 + q

Solving
5 + -12q + 3q2 = 1 + q

Solving for variable 'q'.

Reorder the terms:
5 + -1 + -12q + -1q + 3q2 = 1 + q + -1 + -1q

Combine like terms: 5 + -1 = 4
4 + -12q + -1q + 3q2 = 1 + q + -1 + -1q

Combine like terms: -12q + -1q = -13q
4 + -13q + 3q2 = 1 + q + -1 + -1q

Reorder the terms:
4 + -13q + 3q2 = 1 + -1 + q + -1q

Combine like terms: 1 + -1 = 0
4 + -13q + 3q2 = 0 + q + -1q
4 + -13q + 3q2 = q + -1q

Combine like terms: q + -1q = 0
4 + -13q + 3q2 = 0

Factor a trinomial.
(1 + -3q)(4 + -1q) = 0

Subproblem 1
Set the factor '(1 + -3q)' equal to zero and attempt to solve:

Simplifying
1 + -3q = 0

Solving
1 + -3q = 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 + -3q = 0 + -1

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

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

Divide each side by '-3'.
q = 0.3333333333

Simplifying
q = 0.3333333333
Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

Simplifying
q = 4
Solution
q = {0.3333333333, 4}