How to solve (-a)(-b)(-c)=-abc

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (-a)(-b)(-c)=-abc | Equatix

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Question

$$(-a)(-b)(-c)=-abc$$

Solve for a (complex solution)

$a\in \mathrm{C}$

Solution Steps

Subtract $\left(-a\right)bc$ from both sides.

$$\left(-a\right)\left(-b\right)\left(-c\right)-\left(-a\right)bc=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c-\left(-abc\right)=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c+abc=0$$

Combine $ab\left(-1\right)c$ and $abc$ to get $0$.

$$0=0$$

Compare $0$ and $0$.

$$\text{true}$$

This is true for any $a$.

$$a\in \mathrm{C}$$

Show Solution

Solve for b (complex solution)

$b\in \mathrm{C}$

Solution Steps

Subtract $\left(-a\right)bc$ from both sides.

$$\left(-a\right)\left(-b\right)\left(-c\right)-\left(-a\right)bc=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c-\left(-abc\right)=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c+abc=0$$

Combine $ab\left(-1\right)c$ and $abc$ to get $0$.

$$0=0$$

Compare $0$ and $0$.

$$\text{true}$$

This is true for any $b$.

$$b\in \mathrm{C}$$

Show Solution

Solve for a

$a\in \mathrm{R}$

Solution Steps

Subtract $\left(-a\right)bc$ from both sides.

$$\left(-a\right)\left(-b\right)\left(-c\right)-\left(-a\right)bc=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c-\left(-abc\right)=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c+abc=0$$

Combine $ab\left(-1\right)c$ and $abc$ to get $0$.

$$0=0$$

Compare $0$ and $0$.

$$\text{true}$$

This is true for any $a$.

$$a\in \mathrm{R}$$

Show Solution

Solve for b

$b\in \mathrm{R}$

Solution Steps

Subtract $\left(-a\right)bc$ from both sides.

$$\left(-a\right)\left(-b\right)\left(-c\right)-\left(-a\right)bc=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c-\left(-abc\right)=0$$

Multiply $-1$ and $-1$ to get $1$.

$$ab\left(-1\right)c+abc=0$$

Combine $ab\left(-1\right)c$ and $abc$ to get $0$.

$$0=0$$

Compare $0$ and $0$.

$$\text{true}$$

This is true for any $b$.

$$b\in \mathrm{R}$$

Show Solution

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Example

Question

Solve for a (complex solution)

Solution Steps

Solve for b (complex solution)

Solution Steps

Solve for a

Solution Steps

Solve for b

Solution Steps