460=-5(x+3)(x-24)

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Solution for 460=-5(x+3)(x-24) equation:


Simplifying
460 = -5(x + 3)(x + -24)

Reorder the terms:
460 = -5(3 + x)(x + -24)

Reorder the terms:
460 = -5(3 + x)(-24 + x)

Multiply (3 + x) * (-24 + x)
460 = -5(3(-24 + x) + x(-24 + x))
460 = -5((-24 * 3 + x * 3) + x(-24 + x))
460 = -5((-72 + 3x) + x(-24 + x))
460 = -5(-72 + 3x + (-24 * x + x * x))
460 = -5(-72 + 3x + (-24x + x2))

Combine like terms: 3x + -24x = -21x
460 = -5(-72 + -21x + x2)
460 = (-72 * -5 + -21x * -5 + x2 * -5)
460 = (360 + 105x + -5x2)

Solving
460 = 360 + 105x + -5x2

Solving for variable 'x'.

Combine like terms: 460 + -360 = 100
100 + -105x + 5x2 = 360 + 105x + -5x2 + -360 + -105x + 5x2

Reorder the terms:
100 + -105x + 5x2 = 360 + -360 + 105x + -105x + -5x2 + 5x2

Combine like terms: 360 + -360 = 0
100 + -105x + 5x2 = 0 + 105x + -105x + -5x2 + 5x2
100 + -105x + 5x2 = 105x + -105x + -5x2 + 5x2

Combine like terms: 105x + -105x = 0
100 + -105x + 5x2 = 0 + -5x2 + 5x2
100 + -105x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
100 + -105x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + -21x + x2) = 0

Factor a trinomial.
5((1 + -1x)(20 + -1x)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20

Solution

x = {1, 20}

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