(x+3)(x+5)=x+x+8x+15

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Solution for (x+3)(x+5)=x+x+8x+15 equation: 


Simplifying
(x + 3)(x + 5) = x + x + 8x + 15

Reorder the terms:
(3 + x)(x + 5) = x + x + 8x + 15

Reorder the terms:
(3 + x)(5 + x) = x + x + 8x + 15

Multiply (3 + x) * (5 + x)
(3(5 + x) + x(5 + x)) = x + x + 8x + 15
((5 * 3 + x * 3) + x(5 + x)) = x + x + 8x + 15
((15 + 3x) + x(5 + x)) = x + x + 8x + 15
(15 + 3x + (5 * x + x * x)) = x + x + 8x + 15
(15 + 3x + (5x + x2)) = x + x + 8x + 15

Combine like terms: 3x + 5x = 8x
(15 + 8x + x2) = x + x + 8x + 15

Reorder the terms:
15 + 8x + x2 = 15 + x + x + 8x

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

Combine like terms: 2x + 8x = 10x
15 + 8x + x2 = 15 + 10x

Add '-15' to each side of the equation.
15 + 8x + -15 + x2 = 15 + -15 + 10x

Reorder the terms:
15 + -15 + 8x + x2 = 15 + -15 + 10x

Combine like terms: 15 + -15 = 0
0 + 8x + x2 = 15 + -15 + 10x
8x + x2 = 15 + -15 + 10x

Combine like terms: 15 + -15 = 0
8x + x2 = 0 + 10x
8x + x2 = 10x

Solving
8x + x2 = 10x

Solving for variable 'x'.

Reorder the terms:
8x + -10x + x2 = 10x + -10x

Combine like terms: 8x + -10x = -2x
-2x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-2x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2 + 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2
Solution
x = {0, 2}

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