(x+5)(x-3)=65

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Solution for (x+5)(x-3)=65 equation: 


Simplifying
(x + 5)(x + -3) = 65

Reorder the terms:
(5 + x)(x + -3) = 65

Reorder the terms:
(5 + x)(-3 + x) = 65

Multiply (5 + x) * (-3 + x)
(5(-3 + x) + x(-3 + x)) = 65
((-3 * 5 + x * 5) + x(-3 + x)) = 65
((-15 + 5x) + x(-3 + x)) = 65
(-15 + 5x + (-3 * x + x * x)) = 65
(-15 + 5x + (-3x + x2)) = 65

Combine like terms: 5x + -3x = 2x
(-15 + 2x + x2) = 65

Solving
-15 + 2x + x2 = 65

Solving for variable 'x'.

Reorder the terms:
-15 + -65 + 2x + x2 = 65 + -65

Combine like terms: -15 + -65 = -80
-80 + 2x + x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-80 + 2x + x2 = 0

Factor a trinomial.
(-10 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

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 = {-10, 8}

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