(6q+10)(q-3)=

Solution for (6q+10)(q-3)= equation:

Simplifying
(6q + 10)(q + -3) = 0

Reorder the terms:
(10 + 6q)(q + -3) = 0

Reorder the terms:
(10 + 6q)(-3 + q) = 0

Multiply (10 + 6q) * (-3 + q)
(10(-3 + q) + 6q * (-3 + q)) = 0
((-3 * 10 + q * 10) + 6q * (-3 + q)) = 0
((-30 + 10q) + 6q * (-3 + q)) = 0
(-30 + 10q + (-3 * 6q + q * 6q)) = 0
(-30 + 10q + (-18q + 6q2)) = 0

Combine like terms: 10q + -18q = -8q
(-30 + -8q + 6q2) = 0

Solving
-30 + -8q + 6q2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -4q + 3q2) = 0

Factor a trinomial.
2((-5 + -3q)(3 + -1q)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -3q)' equal to zero and attempt to solve:

Simplifying
-5 + -3q = 0

Solving
-5 + -3q = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3q = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3q = 0 + 5
-3q = 0 + 5

Combine like terms: 0 + 5 = 5
-3q = 5

Divide each side by '-3'.
q = -1.666666667

Simplifying
q = -1.666666667
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 = {-1.666666667, 3}