(x-7)(x+3)=11

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Solution for (x-7)(x+3)=11 equation: 


Simplifying
(x + -7)(x + 3) = 11

Reorder the terms:
(-7 + x)(x + 3) = 11

Reorder the terms:
(-7 + x)(3 + x) = 11

Multiply (-7 + x) * (3 + x)
(-7(3 + x) + x(3 + x)) = 11
((3 * -7 + x * -7) + x(3 + x)) = 11
((-21 + -7x) + x(3 + x)) = 11
(-21 + -7x + (3 * x + x * x)) = 11
(-21 + -7x + (3x + x2)) = 11

Combine like terms: -7x + 3x = -4x
(-21 + -4x + x2) = 11

Solving
-21 + -4x + x2 = 11

Solving for variable 'x'.

Reorder the terms:
-21 + -11 + -4x + x2 = 11 + -11

Combine like terms: -21 + -11 = -32
-32 + -4x + x2 = 11 + -11

Combine like terms: 11 + -11 = 0
-32 + -4x + x2 = 0

Factor a trinomial.
(-4 + -1x)(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-4, 8}

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