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

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


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

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

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

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

Combine like terms: -4x + 2x = -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.
(-5 + -1x)(7 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-5, 7}

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