(x-3)*(x+7)+9=0

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Solution for (x-3)*(x+7)+9=0 equation: 


Simplifying
(x + -3)(x + 7) + 9 = 0

Reorder the terms:
(-3 + x)(x + 7) + 9 = 0

Reorder the terms:
(-3 + x)(7 + x) + 9 = 0

Multiply (-3 + x) * (7 + x)
(-3(7 + x) + x(7 + x)) + 9 = 0
((7 * -3 + x * -3) + x(7 + x)) + 9 = 0
((-21 + -3x) + x(7 + x)) + 9 = 0
(-21 + -3x + (7 * x + x * x)) + 9 = 0
(-21 + -3x + (7x + x2)) + 9 = 0

Combine like terms: -3x + 7x = 4x
(-21 + 4x + x2) + 9 = 0

Reorder the terms:
-21 + 9 + 4x + x2 = 0

Combine like terms: -21 + 9 = -12
-12 + 4x + x2 = 0

Solving
-12 + 4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
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
Solution
x = {-6, 2}

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