x+8=x(x+3)

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


Simplifying
x + 8 = x(x + 3)

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

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

Solving
8 + x = 3x + x2

Solving for variable 'x'.

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

Reorder the terms:
8 + -2x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
8 + -2x + -1x2 = 0 + x2 + -1x2
8 + -2x + -1x2 = x2 + -1x2

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

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

Subproblem 1

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

Subproblem 2

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Solution

x = {2, -4}

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