-x^2-3x+10=x+5

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Solution for -x^2-3x+10=x+5 equation:


Simplifying
-1x2 + -3x + 10 = x + 5

Reorder the terms:
10 + -3x + -1x2 = x + 5

Reorder the terms:
10 + -3x + -1x2 = 5 + x

Solving
10 + -3x + -1x2 = 5 + x

Solving for variable 'x'.

Reorder the terms:
10 + -5 + -3x + -1x + -1x2 = 5 + x + -5 + -1x

Combine like terms: 10 + -5 = 5
5 + -3x + -1x + -1x2 = 5 + x + -5 + -1x

Combine like terms: -3x + -1x = -4x
5 + -4x + -1x2 = 5 + x + -5 + -1x

Reorder the terms:
5 + -4x + -1x2 = 5 + -5 + x + -1x

Combine like terms: 5 + -5 = 0
5 + -4x + -1x2 = 0 + x + -1x
5 + -4x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
5 + -4x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(5 + 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 '(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
Solution
x = {1, -5}

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