x(x+3)=x+8

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Solution for x(x+3)=x+8 equation:


Simplifying
x(x + 3) = x + 8

Reorder the terms:
x(3 + x) = x + 8
(3 * x + x * x) = x + 8
(3x + x2) = x + 8

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

Solving
3x + x2 = 8 + x

Solving for variable 'x'.

Reorder the terms:
-8 + 3x + -1x + x2 = 8 + x + -8 + -1x

Combine like terms: 3x + -1x = 2x
-8 + 2x + x2 = 8 + x + -8 + -1x

Reorder the terms:
-8 + 2x + x2 = 8 + -8 + x + -1x

Combine like terms: 8 + -8 = 0
-8 + 2x + x2 = 0 + x + -1x
-8 + 2x + x2 = x + -1x

Combine like terms: x + -1x = 0
-8 + 2x + x2 = 0

Factor a trinomial.
(-4 + -1x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-4 + -1x)' equal to zero and attempt to solve: Simplifying -4 + -1x = 0 Solving -4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x = 0 + 4 -1x = 0 + 4 Combine like terms: 0 + 4 = 4 -1x = 4 Divide each side by '-1'. x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-4, 2}

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