(x-5)(x+8)=48

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Solution for (x-5)(x+8)=48 equation: 


Simplifying
(x + -5)(x + 8) = 48

Reorder the terms:
(-5 + x)(x + 8) = 48

Reorder the terms:
(-5 + x)(8 + x) = 48

Multiply (-5 + x) * (8 + x)
(-5(8 + x) + x(8 + x)) = 48
((8 * -5 + x * -5) + x(8 + x)) = 48
((-40 + -5x) + x(8 + x)) = 48
(-40 + -5x + (8 * x + x * x)) = 48
(-40 + -5x + (8x + x2)) = 48

Combine like terms: -5x + 8x = 3x
(-40 + 3x + x2) = 48

Solving
-40 + 3x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
-40 + -48 + 3x + x2 = 48 + -48

Combine like terms: -40 + -48 = -88
-88 + 3x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-88 + 3x + x2 = 0

Factor a trinomial.
(-11 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

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 = {-11, 8}

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