(8q-4)(6q+q+1)=

Solution for (8q-4)(6q+q+1)= equation:

Simplifying
(8q + -4)(6q + q + 1) = 0

Reorder the terms:
(-4 + 8q)(6q + q + 1) = 0

Reorder the terms:
(-4 + 8q)(1 + 6q + q) = 0

Combine like terms: 6q + q = 7q
(-4 + 8q)(1 + 7q) = 0

Multiply (-4 + 8q) * (1 + 7q)
(-4(1 + 7q) + 8q * (1 + 7q)) = 0
((1 * -4 + 7q * -4) + 8q * (1 + 7q)) = 0
((-4 + -28q) + 8q * (1 + 7q)) = 0
(-4 + -28q + (1 * 8q + 7q * 8q)) = 0
(-4 + -28q + (8q + 56q2)) = 0

Combine like terms: -28q + 8q = -20q
(-4 + -20q + 56q2) = 0

Solving
-4 + -20q + 56q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -5q + 14q2) = 0

Factor a trinomial.
4((-1 + -7q)(1 + -2q)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -7q)' equal to zero and attempt to solve:

Simplifying
-1 + -7q = 0

Solving
-1 + -7q = 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 + -7q = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7q = 0 + 1
-7q = 0 + 1

Combine like terms: 0 + 1 = 1
-7q = 1

Divide each side by '-7'.
q = -0.1428571429

Simplifying
q = -0.1428571429
Subproblem 2
Set the factor '(1 + -2q)' equal to zero and attempt to solve:

Simplifying
1 + -2q = 0

Solving
1 + -2q = 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 + -2q = 0 + -1

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

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

Divide each side by '-2'.
q = 0.5

Simplifying
q = 0.5
Solution
q = {-0.1428571429, 0.5}