x+3=-x^2+8x-7

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Solution for x+3=-x^2+8x-7 equation: 


Simplifying
x + 3 = -1x2 + 8x + -7

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

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

Solving
3 + x = -7 + 8x + -1x2

Solving for variable 'x'.

Reorder the terms:
3 + 7 + x + -8x + x2 = -7 + 8x + -1x2 + 7 + -8x + x2

Combine like terms: 3 + 7 = 10
10 + x + -8x + x2 = -7 + 8x + -1x2 + 7 + -8x + x2

Combine like terms: x + -8x = -7x
10 + -7x + x2 = -7 + 8x + -1x2 + 7 + -8x + x2

Reorder the terms:
10 + -7x + x2 = -7 + 7 + 8x + -8x + -1x2 + x2

Combine like terms: -7 + 7 = 0
10 + -7x + x2 = 0 + 8x + -8x + -1x2 + x2
10 + -7x + x2 = 8x + -8x + -1x2 + x2

Combine like terms: 8x + -8x = 0
10 + -7x + x2 = 0 + -1x2 + x2
10 + -7x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
10 + -7x + x2 = 0

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


Subproblem 1
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

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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

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