2Q^2-7Q=-5

Solution for 2Q^2-7Q=-5 equation:

Simplifying
2Q2 + -7Q = -5

Reorder the terms:
-7Q + 2Q2 = -5

Solving
-7Q + 2Q2 = -5

Solving for variable 'Q'.

Reorder the terms:
5 + -7Q + 2Q2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + -7Q + 2Q2 = 0

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

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

Simplifying
1 + -1Q = 0

Solving
1 + -1Q = 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 + -1Q = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1Q = 0 + -1
-1Q = 0 + -1

Combine like terms: 0 + -1 = -1
-1Q = -1

Divide each side by '-1'.
Q = 1

Simplifying
Q = 1
Subproblem 2
Set the factor '(5 + -2Q)' equal to zero and attempt to solve:

Simplifying
5 + -2Q = 0

Solving
5 + -2Q = 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 + -2Q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2Q = 0 + -5
-2Q = 0 + -5

Combine like terms: 0 + -5 = -5
-2Q = -5

Divide each side by '-2'.
Q = 2.5

Simplifying
Q = 2.5
Solution
Q = {1, 2.5}