45=x+3+x+5+x^2-3x+4x-3

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Solution for 45=x+3+x+5+x^2-3x+4x-3 equation: 


Simplifying
45 = x + 3 + x + 5 + x2 + -3x + 4x + -3

Reorder the terms:
45 = 3 + 5 + -3 + x + x + -3x + 4x + x2

Combine like terms: 3 + 5 = 8
45 = 8 + -3 + x + x + -3x + 4x + x2

Combine like terms: 8 + -3 = 5
45 = 5 + x + x + -3x + 4x + x2

Combine like terms: x + x = 2x
45 = 5 + 2x + -3x + 4x + x2

Combine like terms: 2x + -3x = -1x
45 = 5 + -1x + 4x + x2

Combine like terms: -1x + 4x = 3x
45 = 5 + 3x + x2

Solving
45 = 5 + 3x + x2

Solving for variable 'x'.

Combine like terms: 45 + -5 = 40
40 + -3x + -1x2 = 5 + 3x + x2 + -5 + -3x + -1x2

Reorder the terms:
40 + -3x + -1x2 = 5 + -5 + 3x + -3x + x2 + -1x2

Combine like terms: 5 + -5 = 0
40 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
40 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
40 + -3x + -1x2 = 0 + x2 + -1x2
40 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + -3x + -1x2 = 0

Factor a trinomial.
(5 + -1x)(8 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

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

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

Simplifying
x = -8
Solution
x = {5, -8}

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