(6sqrt-7)(-10sqrt-12)=

Solution for (6sqrt-7)(-10sqrt-12)= equation:

Simplifying
(6sqrt + -7)(-10sqrt + -12) = 0

Reorder the terms:
(-7 + 6qrst)(-10sqrt + -12) = 0

Reorder the terms:
(-7 + 6qrst)(-12 + -10qrst) = 0

Multiply (-7 + 6qrst) * (-12 + -10qrst)
(-7(-12 + -10qrst) + 6qrst * (-12 + -10qrst)) = 0
((-12 * -7 + -10qrst * -7) + 6qrst * (-12 + -10qrst)) = 0
((84 + 70qrst) + 6qrst * (-12 + -10qrst)) = 0
(84 + 70qrst + (-12 * 6qrst + -10qrst * 6qrst)) = 0
(84 + 70qrst + (-72qrst + -60q2r2s2t2)) = 0

Combine like terms: 70qrst + -72qrst = -2qrst
(84 + -2qrst + -60q2r2s2t2) = 0

Solving
84 + -2qrst + -60q2r2s2t2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), '2'.
2(42 + -1qrst + -30q2r2s2t2) = 0

Factor a trinomial.
2((7 + -6qrst)(6 + 5qrst)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -6qrst)' equal to zero and attempt to solve:

Simplifying
7 + -6qrst = 0

Solving
7 + -6qrst = 0

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

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

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

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

Divide each side by '-6rst'.
q = 1.166666667r-1s-1t-1

Simplifying
q = 1.166666667r-1s-1t-1
Subproblem 2
Set the factor '(6 + 5qrst)' equal to zero and attempt to solve:

Simplifying
6 + 5qrst = 0

Solving
6 + 5qrst = 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 + 5qrst = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5qrst = 0 + -6
5qrst = 0 + -6

Combine like terms: 0 + -6 = -6
5qrst = -6

Divide each side by '5rst'.
q = -1.2r-1s-1t-1

Simplifying
q = -1.2r-1s-1t-1
Solution
q = {1.166666667r-1s-1t-1, -1.2r-1s-1t-1}