-3x(36x^(2)-25)(x^(2)-2)=0

Given Equation: We are given the equation -3x(36x^(2)-25)(x^(2)-2)=0. To solve for x, we will use the Zero Product Property, which states that if the product of several factors is zero, then at least one of the factors must be zero. We have three factors: -3x, (36x^(2)-25), and (x^(2)-2).Factor Zero: First, we set each factor equal to zero separately. The first factor is -3x. Setting -3x equal to zero gives us -3x = 0. Dividing both sides by -3, we find that x = 0.Factor 1 Solution: Next, we set the second factor equal to zero: 36x^(2)-25 = 0. To solve for x, we add 25 to both sides to get 36x^(2) = 25. Then, we divide both sides by 36 to get x^(2) = 25/36. Taking the square root of both sides, we find that x = ±5/6.Factor 2 Solution: Finally, we set the third factor equal to zero: x^(2)-2 = 0. Adding 2 to both sides gives us x^(2) = 2. Taking the square root of both sides, we find that x = ±√2.

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$-3 x\left(36 x^{2}-25\right)\left(x^{2}-2\right)=0$

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-3 x\left(36 x^{2}-25\right)\left(x^{2}-2\right)=0

Given Equation: We are given the equation $-3x(36x^{2}-25)(x^{2}-2)=0$ . To solve for $x$ , we will use the Zero Product Property, which states that if the product of several factors is zero, then at least one of the factors must be zero. We have three factors: $-3x$ , $(36x^{2}-25)$ , and $(x^{2}-2)$ .
Factor Zero: First, we set each factor equal to zero separately. The first factor is $-3x$ . Setting $-3x$ equal to zero gives us $-3x = 0$ . Dividing both sides by $-3$ , we find that $x = 0$ .
Factor $1$ Solution: Next, we set the second factor equal to zero: $36x^{2}-25 = 0$ . To solve for $x$ , we add $25$ to both sides to get $36x^{2} = 25$ . Then, we divide both sides by $36$ to get $x^{2} = \frac{25}{36}$ . Taking the square root of both sides, we find that $x = \pm\frac{5}{6}$ .
Factor $2$ Solution: Finally, we set the third factor equal to zero: $x^{2}-2 = 0$ . Adding $2$ to both sides gives us $x^{2} = 2$ . Taking the square root of both sides, we find that $x = \pm\sqrt{2}$ .