(x+3)(x-5)+7=0

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Solution for (x+3)(x-5)+7=0 equation: 


Simplifying
(x + 3)(x + -5) + 7 = 0

Reorder the terms:
(3 + x)(x + -5) + 7 = 0

Reorder the terms:
(3 + x)(-5 + x) + 7 = 0

Multiply (3 + x) * (-5 + x)
(3(-5 + x) + x(-5 + x)) + 7 = 0
((-5 * 3 + x * 3) + x(-5 + x)) + 7 = 0
((-15 + 3x) + x(-5 + x)) + 7 = 0
(-15 + 3x + (-5 * x + x * x)) + 7 = 0
(-15 + 3x + (-5x + x2)) + 7 = 0

Combine like terms: 3x + -5x = -2x
(-15 + -2x + x2) + 7 = 0

Reorder the terms:
-15 + 7 + -2x + x2 = 0

Combine like terms: -15 + 7 = -8
-8 + -2x + x2 = 0

Solving
-8 + -2x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 4}

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