(-7x+3)-(x^2+x-6)=

Solution for (-7x+3)-(x^2+x-6)= equation:

Simplifying
(-7x + 3) + -1(x2 + x + -6) = 0

Reorder the terms:
(3 + -7x) + -1(x2 + x + -6) = 0

Remove parenthesis around (3 + -7x)
3 + -7x + -1(x2 + x + -6) = 0

Reorder the terms:
3 + -7x + -1(-6 + x + x2) = 0
3 + -7x + (-6 * -1 + x * -1 + x2 * -1) = 0
3 + -7x + (6 + -1x + -1x2) = 0

Reorder the terms:
3 + 6 + -7x + -1x + -1x2 = 0

Combine like terms: 3 + 6 = 9
9 + -7x + -1x + -1x2 = 0

Combine like terms: -7x + -1x = -8x
9 + -8x + -1x2 = 0

Solving
9 + -8x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(9 + x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(9 + x)' equal to zero and attempt to solve:

Simplifying
9 + x = 0

Solving
9 + x = 0

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

Add '-9' to each side of the equation.
9 + -9 + x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + x = 0 + -9
x = 0 + -9

Combine like terms: 0 + -9 = -9
x = -9

Simplifying
x = -9
Solution
x = {1, -9}