Solve 5(x)^(2)-20+(x-1)(6-3x)-(3x+1)(x-2) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$5 { x }^{ 2 } -20+(x-1)(6-3x)-(3x+1)(x-2)$$

Evaluate

$\left(2-x\right)\left(x-12\right)$

Solution Steps

Use the distributive property to multiply $x-1$ by $6-3x$ and combine like terms.

$$5x^{2}-20+9x-3x^{2}-6-\left(3x+1\right)\left(x-2\right)$$

Combine $5x^{2}$ and $-3x^{2}$ to get $2x^{2}$.

$$2x^{2}-20+9x-6-\left(3x+1\right)\left(x-2\right)$$

Subtract $6$ from $-20$ to get $-26$.

$$2x^{2}-26+9x-\left(3x+1\right)\left(x-2\right)$$

Use the distributive property to multiply $3x+1$ by $x-2$ and combine like terms.

$$2x^{2}-26+9x-\left(3x^{2}-5x-2\right)$$

To find the opposite of $3x^{2}-5x-2$, find the opposite of each term.

$$2x^{2}-26+9x-3x^{2}+5x+2$$

Combine $2x^{2}$ and $-3x^{2}$ to get $-x^{2}$.

$$-x^{2}-26+9x+5x+2$$

Combine $9x$ and $5x$ to get $14x$.

$$-x^{2}-26+14x+2$$

Add $-26$ and $2$ to get $-24$.

$$-x^{2}-24+14x$$

Expand

$-x^{2}+14x-24$

Solution Steps

Use the distributive property to multiply $x-1$ by $6-3x$ and combine like terms.

$$5x^{2}-20+9x-3x^{2}-6-\left(3x+1\right)\left(x-2\right)$$

Combine $5x^{2}$ and $-3x^{2}$ to get $2x^{2}$.

$$2x^{2}-20+9x-6-\left(3x+1\right)\left(x-2\right)$$

Subtract $6$ from $-20$ to get $-26$.

$$2x^{2}-26+9x-\left(3x+1\right)\left(x-2\right)$$

Use the distributive property to multiply $3x+1$ by $x-2$ and combine like terms.

$$2x^{2}-26+9x-\left(3x^{2}-5x-2\right)$$

To find the opposite of $3x^{2}-5x-2$, find the opposite of each term.

$$2x^{2}-26+9x-3x^{2}+5x+2$$

Combine $2x^{2}$ and $-3x^{2}$ to get $-x^{2}$.

$$-x^{2}-26+9x+5x+2$$

Combine $9x$ and $5x$ to get $14x$.

$$-x^{2}-26+14x+2$$

Add $-26$ and $2$ to get $-24$.

$$-x^{2}-24+14x$$