7x-3=5-x^2

Solution for 7x-3=5-x^2 equation:

Simplifying
7x + -3 = 5 + -1x2

Reorder the terms:
-3 + 7x = 5 + -1x2

Solving
-3 + 7x = 5 + -1x2

Solving for variable 'x'.

Reorder the terms:
-3 + -5 + 7x + x2 = 5 + -1x2 + -5 + x2

Combine like terms: -3 + -5 = -8
-8 + 7x + x2 = 5 + -1x2 + -5 + x2

Reorder the terms:
-8 + 7x + x2 = 5 + -5 + -1x2 + x2

Combine like terms: 5 + -5 = 0
-8 + 7x + x2 = 0 + -1x2 + x2
-8 + 7x + x2 = -1x2 + x2

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

Factor a trinomial.
(-8 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
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
Solution
x = {-8, 1}