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

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


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

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

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

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

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

Solving
-15 + 2x + x2 = -7

Solving for variable 'x'.

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

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-4, 2}

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