3x*x+5x=24-x

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Solution for 3x*x+5x=24-x equation:


Simplifying
3x * x + 5x = 24 + -1x

Multiply x * x
3x2 + 5x = 24 + -1x

Reorder the terms:
5x + 3x2 = 24 + -1x

Solving
5x + 3x2 = 24 + -1x

Solving for variable 'x'.

Reorder the terms:
-24 + 5x + x + 3x2 = 24 + -1x + -24 + x

Combine like terms: 5x + x = 6x
-24 + 6x + 3x2 = 24 + -1x + -24 + x

Reorder the terms:
-24 + 6x + 3x2 = 24 + -24 + -1x + x

Combine like terms: 24 + -24 = 0
-24 + 6x + 3x2 = 0 + -1x + x
-24 + 6x + 3x2 = -1x + x

Combine like terms: -1x + x = 0
-24 + 6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 2x + x2) = 0

Factor a trinomial.
3((-4 + -1x)(2 + -1x)) = 0

Ignore the factor 3.

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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