-X^2+7X=10

Solution for -X^2+7X=10 equation:

Simplifying
-1X2 + 7X = 10

Reorder the terms:
7X + -1X2 = 10

Solving
7X + -1X2 = 10

Solving for variable 'X'.

Reorder the terms:
-10 + 7X + -1X2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 7X + -1X2 = 0

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

Subproblem 1
Set the factor '(-5 + X)' equal to zero and attempt to solve:

Simplifying
-5 + X = 0

Solving
-5 + X = 0

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

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

Combine like terms: -5 + 5 = 0
0 + X = 0 + 5
X = 0 + 5

Combine like terms: 0 + 5 = 5
X = 5

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

Simplifying
2 + -1X = 0

Solving
2 + -1X = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1X = 0 + -2
-1X = 0 + -2

Combine like terms: 0 + -2 = -2
-1X = -2

Divide each side by '-1'.
X = 2

Simplifying
X = 2
Solution
X = {5, 2}