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

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


Simplifying
2x + 3 = x2 + 4x + -5

Reorder the terms:
3 + 2x = x2 + 4x + -5

Reorder the terms:
3 + 2x = -5 + 4x + x2

Solving
3 + 2x = -5 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
3 + 5 + 2x + -4x + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2

Combine like terms: 3 + 5 = 8
8 + 2x + -4x + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2

Combine like terms: 2x + -4x = -2x
8 + -2x + -1x2 = -5 + 4x + x2 + 5 + -4x + -1x2

Reorder the terms:
8 + -2x + -1x2 = -5 + 5 + 4x + -4x + x2 + -1x2

Combine like terms: -5 + 5 = 0
8 + -2x + -1x2 = 0 + 4x + -4x + x2 + -1x2
8 + -2x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
8 + -2x + -1x2 = 0 + x2 + -1x2
8 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
8 + -2x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(4 + 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 '(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 = {2, -4}

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