(x+6)(x+4)=-1

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Solution for (x+6)(x+4)=-1 equation:


Simplifying
(x + 6)(x + 4) = -1

Reorder the terms:
(6 + x)(x + 4) = -1

Reorder the terms:
(6 + x)(4 + x) = -1

Multiply (6 + x) * (4 + x)
(6(4 + x) + x(4 + x)) = -1
((4 * 6 + x * 6) + x(4 + x)) = -1
((24 + 6x) + x(4 + x)) = -1
(24 + 6x + (4 * x + x * x)) = -1
(24 + 6x + (4x + x2)) = -1

Combine like terms: 6x + 4x = 10x
(24 + 10x + x2) = -1

Solving
24 + 10x + x2 = -1

Solving for variable 'x'.

Reorder the terms:
24 + 1 + 10x + x2 = -1 + 1

Combine like terms: 24 + 1 = 25
25 + 10x + x2 = -1 + 1

Combine like terms: -1 + 1 = 0
25 + 10x + x2 = 0

Factor a trinomial.
(5 + x)(5 + x) = 0

Subproblem 1

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

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 = {-5, -5}

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