(x-2)(x+4)=27

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Solution for (x-2)(x+4)=27 equation: 


Simplifying
(x + -2)(x + 4) = 27

Reorder the terms:
(-2 + x)(x + 4) = 27

Reorder the terms:
(-2 + x)(4 + x) = 27

Multiply (-2 + x) * (4 + x)
(-2(4 + x) + x(4 + x)) = 27
((4 * -2 + x * -2) + x(4 + x)) = 27
((-8 + -2x) + x(4 + x)) = 27
(-8 + -2x + (4 * x + x * x)) = 27
(-8 + -2x + (4x + x2)) = 27

Combine like terms: -2x + 4x = 2x
(-8 + 2x + x2) = 27

Solving
-8 + 2x + x2 = 27

Solving for variable 'x'.

Reorder the terms:
-8 + -27 + 2x + x2 = 27 + -27

Combine like terms: -8 + -27 = -35
-35 + 2x + x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-35 + 2x + x2 = 0

Factor a trinomial.
(-7 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-7, 5}

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