4+2x=5(x-3)+x^2+9

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Solution for 4+2x=5(x-3)+x^2+9 equation: 


Simplifying
4 + 2x = 5(x + -3) + x2 + 9

Reorder the terms:
4 + 2x = 5(-3 + x) + x2 + 9
4 + 2x = (-3 * 5 + x * 5) + x2 + 9
4 + 2x = (-15 + 5x) + x2 + 9

Reorder the terms:
4 + 2x = -15 + 9 + 5x + x2

Combine like terms: -15 + 9 = -6
4 + 2x = -6 + 5x + x2

Solving
4 + 2x = -6 + 5x + x2

Solving for variable 'x'.

Reorder the terms:
4 + 6 + 2x + -5x + -1x2 = -6 + 5x + x2 + 6 + -5x + -1x2

Combine like terms: 4 + 6 = 10
10 + 2x + -5x + -1x2 = -6 + 5x + x2 + 6 + -5x + -1x2

Combine like terms: 2x + -5x = -3x
10 + -3x + -1x2 = -6 + 5x + x2 + 6 + -5x + -1x2

Reorder the terms:
10 + -3x + -1x2 = -6 + 6 + 5x + -5x + x2 + -1x2

Combine like terms: -6 + 6 = 0
10 + -3x + -1x2 = 0 + 5x + -5x + x2 + -1x2
10 + -3x + -1x2 = 5x + -5x + x2 + -1x2

Combine like terms: 5x + -5x = 0
10 + -3x + -1x2 = 0 + x2 + -1x2
10 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -3x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(5 + x) = 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 + 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 = {2, -5}

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