-x^2+5x+1=2x-3

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Solution for -x^2+5x+1=2x-3 equation:


Simplifying
-1x2 + 5x + 1 = 2x + -3

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

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

Solving
1 + 5x + -1x2 = -3 + 2x

Solving for variable 'x'.

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

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

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

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

Combine like terms: -3 + 3 = 0
4 + 3x + -1x2 = 0 + 2x + -2x
4 + 3x + -1x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
4 + 3x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(1 + x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

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

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