x*x+4x-21=x+7

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Solution for x*x+4x-21=x+7 equation: 


Simplifying
x * x + 4x + -21 = x + 7

Multiply x * x
x2 + 4x + -21 = x + 7

Reorder the terms:
-21 + 4x + x2 = x + 7

Reorder the terms:
-21 + 4x + x2 = 7 + x

Solving
-21 + 4x + x2 = 7 + x

Solving for variable 'x'.

Reorder the terms:
-21 + -7 + 4x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: -21 + -7 = -28
-28 + 4x + -1x + x2 = 7 + x + -7 + -1x

Combine like terms: 4x + -1x = 3x
-28 + 3x + x2 = 7 + x + -7 + -1x

Reorder the terms:
-28 + 3x + x2 = 7 + -7 + x + -1x

Combine like terms: 7 + -7 = 0
-28 + 3x + x2 = 0 + x + -1x
-28 + 3x + x2 = x + -1x

Combine like terms: x + -1x = 0
-28 + 3x + x2 = 0

Factor a trinomial.
(-7 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-7, 4}

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