8x+24=x*x+6x

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Solution for 8x+24=x*x+6x equation:


Simplifying
8x + 24 = x * x + 6x

Reorder the terms:
24 + 8x = x * x + 6x

Multiply x * x
24 + 8x = x2 + 6x

Reorder the terms:
24 + 8x = 6x + x2

Solving
24 + 8x = 6x + x2

Solving for variable 'x'.

Combine like terms: 8x + -6x = 2x
24 + 2x + -1x2 = 6x + x2 + -6x + -1x2

Reorder the terms:
24 + 2x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
24 + 2x + -1x2 = 0 + x2 + -1x2
24 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 2x + -1x2 = 0

Factor a trinomial.
(6 + -1x)(4 + x) = 0

Subproblem 1

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

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 = {6, -4}

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