3q^2=-q+140

Solution for 3q^2=-q+140 equation:

Simplifying
3q2 = -1q + 140

Reorder the terms:
3q2 = 140 + -1q

Solving
3q2 = 140 + -1q

Solving for variable 'q'.

Reorder the terms:
-140 + q + 3q2 = 140 + -1q + -140 + q

Reorder the terms:
-140 + q + 3q2 = 140 + -140 + -1q + q

Combine like terms: 140 + -140 = 0
-140 + q + 3q2 = 0 + -1q + q
-140 + q + 3q2 = -1q + q

Combine like terms: -1q + q = 0
-140 + q + 3q2 = 0

Factor a trinomial.
(-7 + -1q)(20 + -3q) = 0

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

Simplifying
-7 + -1q = 0

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

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

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

Divide each side by '-1'.
q = -7

Simplifying
q = -7
Subproblem 2
Set the factor '(20 + -3q)' equal to zero and attempt to solve:

Simplifying
20 + -3q = 0

Solving
20 + -3q = 0

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

Add '-20' to each side of the equation.
20 + -20 + -3q = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -3q = 0 + -20
-3q = 0 + -20

Combine like terms: 0 + -20 = -20
-3q = -20

Divide each side by '-3'.
q = 6.666666667

Simplifying
q = 6.666666667
Solution
q = {-7, 6.666666667}