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

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


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

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

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

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

Combine like terms: -3x + 7x = 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.
(-8 + -1x)(4 + -1x) = 0


Subproblem 1
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

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 = {-8, 4}

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