-3(2q-4)=-5q(q+7)

Solution for -3(2q-4)=-5q(q+7) equation:

Simplifying
-3(2q + -4) = -5q(q + 7)

Reorder the terms:
-3(-4 + 2q) = -5q(q + 7)
(-4 * -3 + 2q * -3) = -5q(q + 7)
(12 + -6q) = -5q(q + 7)

Reorder the terms:
12 + -6q = -5q(7 + q)
12 + -6q = (7 * -5q + q * -5q)
12 + -6q = (-35q + -5q2)

Solving
12 + -6q = -35q + -5q2

Solving for variable 'q'.

Combine like terms: -6q + 35q = 29q
12 + 29q + 5q2 = -35q + -5q2 + 35q + 5q2

Reorder the terms:
12 + 29q + 5q2 = -35q + 35q + -5q2 + 5q2

Combine like terms: -35q + 35q = 0
12 + 29q + 5q2 = 0 + -5q2 + 5q2
12 + 29q + 5q2 = -5q2 + 5q2

Combine like terms: -5q2 + 5q2 = 0
12 + 29q + 5q2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2.4 + 5.8q + q2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + 5.8q + -2.4 + q2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + 5.8q + q2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + 5.8q + q2 = 0 + -2.4
5.8q + q2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
5.8q + q2 = -2.4

The q term is 5.8q.  Take half its coefficient (2.9).
Square it (8.41) and add it to both sides.

Add '8.41' to each side of the equation.
5.8q + 8.41 + q2 = -2.4 + 8.41

Reorder the terms:
8.41 + 5.8q + q2 = -2.4 + 8.41

Combine like terms: -2.4 + 8.41 = 6.01
8.41 + 5.8q + q2 = 6.01

Factor a perfect square on the left side:
(q + 2.9)(q + 2.9) = 6.01

Calculate the square root of the right side: 2.451530134

Break this problem into two subproblems by setting 
(q + 2.9) equal to 2.451530134 and -2.451530134.

Subproblem 1
q + 2.9 = 2.451530134

Simplifying
q + 2.9 = 2.451530134

Reorder the terms:
2.9 + q = 2.451530134

Solving
2.9 + q = 2.451530134

Solving for variable 'q'.

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

Add '-2.9' to each side of the equation.
2.9 + -2.9 + q = 2.451530134 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + q = 2.451530134 + -2.9
q = 2.451530134 + -2.9

Combine like terms: 2.451530134 + -2.9 = -0.448469866
q = -0.448469866

Simplifying
q = -0.448469866

Subproblem 2
q + 2.9 = -2.451530134

Simplifying
q + 2.9 = -2.451530134

Reorder the terms:
2.9 + q = -2.451530134

Solving
2.9 + q = -2.451530134

Solving for variable 'q'.

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

Add '-2.9' to each side of the equation.
2.9 + -2.9 + q = -2.451530134 + -2.9

Combine like terms: 2.9 + -2.9 = 0.0
0.0 + q = -2.451530134 + -2.9
q = -2.451530134 + -2.9

Combine like terms: -2.451530134 + -2.9 = -5.351530134
q = -5.351530134

Simplifying
q = -5.351530134

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {-0.448469866, -5.351530134}