(x+3)(x-5)=20

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Solution for (x+3)(x-5)=20 equation: 


Simplifying
(x + 3)(x + -5) = 20

Reorder the terms:
(3 + x)(x + -5) = 20

Reorder the terms:
(3 + x)(-5 + x) = 20

Multiply (3 + x) * (-5 + x)
(3(-5 + x) + x(-5 + x)) = 20
((-5 * 3 + x * 3) + x(-5 + x)) = 20
((-15 + 3x) + x(-5 + x)) = 20
(-15 + 3x + (-5 * x + x * x)) = 20
(-15 + 3x + (-5x + x2)) = 20

Combine like terms: 3x + -5x = -2x
(-15 + -2x + x2) = 20

Solving
-15 + -2x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
-15 + -20 + -2x + x2 = 20 + -20

Combine like terms: -15 + -20 = -35
-35 + -2x + x2 = 20 + -20

Combine like terms: 20 + -20 = 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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