0=2x(x-3)(x+5)

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Solution for 0=2x(x-3)(x+5) equation:


Simplifying
0 = 2x(x + -3)(x + 5)

Reorder the terms:
0 = 2x(-3 + x)(x + 5)

Reorder the terms:
0 = 2x(-3 + x)(5 + x)

Multiply (-3 + x) * (5 + x)
0 = 2x(-3(5 + x) + x(5 + x))
0 = 2x((5 * -3 + x * -3) + x(5 + x))
0 = 2x((-15 + -3x) + x(5 + x))
0 = 2x(-15 + -3x + (5 * x + x * x))
0 = 2x(-15 + -3x + (5x + x2))

Combine like terms: -3x + 5x = 2x
0 = 2x(-15 + 2x + x2)
0 = (-15 * 2x + 2x * 2x + x2 * 2x)
0 = (-30x + 4x2 + 2x3)

Solving
0 = -30x + 4x2 + 2x3

Solving for variable 'x'.
Remove the zero:
30x + -4x2 + -2x3 = -30x + 4x2 + 2x3 + 30x + -4x2 + -2x3

Reorder the terms:
30x + -4x2 + -2x3 = -30x + 30x + 4x2 + -4x2 + 2x3 + -2x3

Combine like terms: -30x + 30x = 0
30x + -4x2 + -2x3 = 0 + 4x2 + -4x2 + 2x3 + -2x3
30x + -4x2 + -2x3 = 4x2 + -4x2 + 2x3 + -2x3

Combine like terms: 4x2 + -4x2 = 0
30x + -4x2 + -2x3 = 0 + 2x3 + -2x3
30x + -4x2 + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
30x + -4x2 + -2x3 = 0

Factor out the Greatest Common Factor (GCF), '2x'.
2x(15 + -2x + -1x2) = 0

Factor a trinomial.
2x((3 + -1x)(5 + x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

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 3

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {0, 3, -5}

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