-x^2-8x+24=-2x^2+3x

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Solution for -x^2-8x+24=-2x^2+3x equation:


Simplifying
-1x2 + -8x + 24 = -2x2 + 3x

Reorder the terms:
24 + -8x + -1x2 = -2x2 + 3x

Reorder the terms:
24 + -8x + -1x2 = 3x + -2x2

Solving
24 + -8x + -1x2 = 3x + -2x2

Solving for variable 'x'.

Reorder the terms:
24 + -8x + -3x + -1x2 + 2x2 = 3x + -2x2 + -3x + 2x2

Combine like terms: -8x + -3x = -11x
24 + -11x + -1x2 + 2x2 = 3x + -2x2 + -3x + 2x2

Combine like terms: -1x2 + 2x2 = 1x2
24 + -11x + 1x2 = 3x + -2x2 + -3x + 2x2

Reorder the terms:
24 + -11x + 1x2 = 3x + -3x + -2x2 + 2x2

Combine like terms: 3x + -3x = 0
24 + -11x + 1x2 = 0 + -2x2 + 2x2
24 + -11x + 1x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
24 + -11x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

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

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

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {3, 8}

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