0=21+4x-x^2

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Solution for 0=21+4x-x^2 equation: 


Simplifying
0 = 21 + 4x + -1x2

Solving
0 = 21 + 4x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -21 = -21
-21 + -4x + x2 = 21 + 4x + -1x2 + -21 + -4x + x2

Reorder the terms:
-21 + -4x + x2 = 21 + -21 + 4x + -4x + -1x2 + x2

Combine like terms: 21 + -21 = 0
-21 + -4x + x2 = 0 + 4x + -4x + -1x2 + x2
-21 + -4x + x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
-21 + -4x + x2 = 0 + -1x2 + x2
-21 + -4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-21 + -4x + x2 = 0

Factor a trinomial.
(-3 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-3, 7}

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