x(x-2)(3+4x)=

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Solution for x(x-2)(3+4x)= equation:


Simplifying
x(x + -2)(3 + 4x) = 0

Reorder the terms:
x(-2 + x)(3 + 4x) = 0

Multiply (-2 + x) * (3 + 4x)
x(-2(3 + 4x) + x(3 + 4x)) = 0
x((3 * -2 + 4x * -2) + x(3 + 4x)) = 0
x((-6 + -8x) + x(3 + 4x)) = 0
x(-6 + -8x + (3 * x + 4x * x)) = 0
x(-6 + -8x + (3x + 4x2)) = 0

Combine like terms: -8x + 3x = -5x
x(-6 + -5x + 4x2) = 0
(-6 * x + -5x * x + 4x2 * x) = 0
(-6x + -5x2 + 4x3) = 0

Solving
-6x + -5x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-6 + -5x + 4x2) = 0

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

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 + -4x)' equal to zero and attempt to solve: Simplifying -3 + -4x = 0 Solving -3 + -4x = 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 + -4x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4x = 0 + 3 -4x = 0 + 3 Combine like terms: 0 + 3 = 3 -4x = 3 Divide each side by '-4'. x = -0.75 Simplifying x = -0.75

Subproblem 3

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 = {0, -0.75, 2}

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