(x-5)(x+3)=105

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Solution for (x-5)(x+3)=105 equation: 


Simplifying
(x + -5)(x + 3) = 105

Reorder the terms:
(-5 + x)(x + 3) = 105

Reorder the terms:
(-5 + x)(3 + x) = 105

Multiply (-5 + x) * (3 + x)
(-5(3 + x) + x(3 + x)) = 105
((3 * -5 + x * -5) + x(3 + x)) = 105
((-15 + -5x) + x(3 + x)) = 105
(-15 + -5x + (3 * x + x * x)) = 105
(-15 + -5x + (3x + x2)) = 105

Combine like terms: -5x + 3x = -2x
(-15 + -2x + x2) = 105

Solving
-15 + -2x + x2 = 105

Solving for variable 'x'.

Reorder the terms:
-15 + -105 + -2x + x2 = 105 + -105

Combine like terms: -15 + -105 = -120
-120 + -2x + x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-120 + -2x + x2 = 0

Factor a trinomial.
(-10 + -1x)(12 + -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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-10, 12}

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