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

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


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

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

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

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

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

Solving
15 + 8x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
15 + -3 + 8x + x2 = 3 + -3

Combine like terms: 15 + -3 = 12
12 + 8x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
12 + 8x + x2 = 0

Factor a trinomial.
(6 + x)(2 + x) = 0

Subproblem 1

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

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 = {-6, -2}

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