(2x+3)(x+5)=15

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Solution for (2x+3)(x+5)=15 equation: 


Simplifying
(2x + 3)(x + 5) = 15

Reorder the terms:
(3 + 2x)(x + 5) = 15

Reorder the terms:
(3 + 2x)(5 + x) = 15

Multiply (3 + 2x) * (5 + x)
(3(5 + x) + 2x * (5 + x)) = 15
((5 * 3 + x * 3) + 2x * (5 + x)) = 15
((15 + 3x) + 2x * (5 + x)) = 15
(15 + 3x + (5 * 2x + x * 2x)) = 15
(15 + 3x + (10x + 2x2)) = 15

Combine like terms: 3x + 10x = 13x
(15 + 13x + 2x2) = 15

Add '-15' to each side of the equation.
15 + 13x + -15 + 2x2 = 15 + -15

Reorder the terms:
15 + -15 + 13x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
0 + 13x + 2x2 = 15 + -15
13x + 2x2 = 15 + -15

Combine like terms: 15 + -15 = 0
13x + 2x2 = 0

Solving
13x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(13 + 2x) = 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 '(13 + 2x)' equal to zero and attempt to solve:

Simplifying
13 + 2x = 0

Solving
13 + 2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2x = 0 + -13
2x = 0 + -13

Combine like terms: 0 + -13 = -13
2x = -13

Divide each side by '2'.
x = -6.5

Simplifying
x = -6.5
Solution
x = {0, -6.5}

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