(x-3)(x+5)=x-7x-15

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Solution for (x-3)(x+5)=x-7x-15 equation:


Simplifying
(x + -3)(x + 5) = x + -7x + -15

Reorder the terms:
(-3 + x)(x + 5) = x + -7x + -15

Reorder the terms:
(-3 + x)(5 + x) = x + -7x + -15

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

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

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

Combine like terms: x + -7x = -6x
-15 + 2x + x2 = -15 + -6x

Add '15' to each side of the equation.
-15 + 2x + 15 + x2 = -15 + 15 + -6x

Reorder the terms:
-15 + 15 + 2x + x2 = -15 + 15 + -6x

Combine like terms: -15 + 15 = 0
0 + 2x + x2 = -15 + 15 + -6x
2x + x2 = -15 + 15 + -6x

Combine like terms: -15 + 15 = 0
2x + x2 = 0 + -6x
2x + x2 = -6x

Solving
2x + x2 = -6x

Solving for variable 'x'.

Reorder the terms:
2x + 6x + x2 = -6x + 6x

Combine like terms: 2x + 6x = 8x
8x + x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
8x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(8 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(8 + x)' equal to zero and attempt to solve:

Simplifying
8 + x = 0

Solving
8 + x = 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 + x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {0, -8}

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