(x+8)(x-2)=-21

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Solution for (x+8)(x-2)=-21 equation:


Simplifying
(x + 8)(x + -2) = -21

Reorder the terms:
(8 + x)(x + -2) = -21

Reorder the terms:
(8 + x)(-2 + x) = -21

Multiply (8 + x) * (-2 + x)
(8(-2 + x) + x(-2 + x)) = -21
((-2 * 8 + x * 8) + x(-2 + x)) = -21
((-16 + 8x) + x(-2 + x)) = -21
(-16 + 8x + (-2 * x + x * x)) = -21
(-16 + 8x + (-2x + x2)) = -21

Combine like terms: 8x + -2x = 6x
(-16 + 6x + x2) = -21

Solving
-16 + 6x + x2 = -21

Solving for variable 'x'.

Reorder the terms:
-16 + 21 + 6x + x2 = -21 + 21

Combine like terms: -16 + 21 = 5
5 + 6x + x2 = -21 + 21

Combine like terms: -21 + 21 = 0
5 + 6x + x2 = 0

Factor a trinomial.
(5 + x)(1 + 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 '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {-5, -1}

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