-x^2+15=3x+11

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Solution for -x^2+15=3x+11 equation: 


Simplifying
-1x2 + 15 = 3x + 11

Reorder the terms:
15 + -1x2 = 3x + 11

Reorder the terms:
15 + -1x2 = 11 + 3x

Solving
15 + -1x2 = 11 + 3x

Solving for variable 'x'.

Reorder the terms:
15 + -11 + -3x + -1x2 = 11 + 3x + -11 + -3x

Combine like terms: 15 + -11 = 4
4 + -3x + -1x2 = 11 + 3x + -11 + -3x

Reorder the terms:
4 + -3x + -1x2 = 11 + -11 + 3x + -3x

Combine like terms: 11 + -11 = 0
4 + -3x + -1x2 = 0 + 3x + -3x
4 + -3x + -1x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
4 + -3x + -1x2 = 0

Factor a trinomial.
(1 + -1x)(4 + 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {1, -4}

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