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

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


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

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

Reorder the terms:
15 + 3x = 3x(5 + x)
15 + 3x = (5 * 3x + x * 3x)
15 + 3x = (15x + 3x2)

Solving
15 + 3x = 15x + 3x2

Solving for variable 'x'.

Combine like terms: 3x + -15x = -12x
15 + -12x + -3x2 = 15x + 3x2 + -15x + -3x2

Reorder the terms:
15 + -12x + -3x2 = 15x + -15x + 3x2 + -3x2

Combine like terms: 15x + -15x = 0
15 + -12x + -3x2 = 0 + 3x2 + -3x2
15 + -12x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
15 + -12x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -4x + -1x2) = 0

Factor a trinomial.
3((1 + -1x)(5 + x)) = 0

Ignore the factor 3.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {1, -5}

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