(7q-6)(4q-5)=0

Solution for (7q-6)(4q-5)=0 equation:

Simplifying
(7q + -6)(4q + -5) = 0

Reorder the terms:
(-6 + 7q)(4q + -5) = 0

Reorder the terms:
(-6 + 7q)(-5 + 4q) = 0

Multiply (-6 + 7q) * (-5 + 4q)
(-6(-5 + 4q) + 7q * (-5 + 4q)) = 0
((-5 * -6 + 4q * -6) + 7q * (-5 + 4q)) = 0
((30 + -24q) + 7q * (-5 + 4q)) = 0
(30 + -24q + (-5 * 7q + 4q * 7q)) = 0
(30 + -24q + (-35q + 28q2)) = 0

Combine like terms: -24q + -35q = -59q
(30 + -59q + 28q2) = 0

Solving
30 + -59q + 28q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(6 + -7q)(5 + -4q) = 0

Subproblem 1
Set the factor '(6 + -7q)' equal to zero and attempt to solve:

Simplifying
6 + -7q = 0

Solving
6 + -7q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7q = 0 + -6
-7q = 0 + -6

Combine like terms: 0 + -6 = -6
-7q = -6

Divide each side by '-7'.
q = 0.8571428571

Simplifying
q = 0.8571428571
Subproblem 2
Set the factor '(5 + -4q)' equal to zero and attempt to solve:

Simplifying
5 + -4q = 0

Solving
5 + -4q = 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 + -4q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4q = 0 + -5
-4q = 0 + -5

Combine like terms: 0 + -5 = -5
-4q = -5

Divide each side by '-4'.
q = 1.25

Simplifying
q = 1.25
Solution
q = {0.8571428571, 1.25}