Solve (x+2)(x+3)+(x-3)(x-2)-2x(x+7=0 | 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

$$(x+2)(x+3)+(x-3)(x-2)-2x(x+7=0$$

Solve for x

$x=6$

Steps for Solving Linear Equation

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

$$x^{2}+5x+6+\left(x-3\right)\left(x-2\right)-2x\left(x+1\right)=0$$

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

$$x^{2}+5x+6+x^{2}-5x+6-2x\left(x+1\right)=0$$

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

$$2x^{2}+5x+6-5x+6-2x\left(x+1\right)=0$$

Combine $5x$ and $-5x$ to get $0$.

$$2x^{2}+6+6-2x\left(x+1\right)=0$$

Add $6$ and $6$ to get $12$.

$$2x^{2}+12-2x\left(x+1\right)=0$$

Use the distributive property to multiply $-2x$ by $x+1$.

$$2x^{2}+12-2x^{2}-2x=0$$

Combine $2x^{2}$ and $-2x^{2}$ to get $0$.

$$12-2x=0$$

Subtract $12$ from both sides. Anything subtracted from zero gives its negation.

$$-2x=-12$$

Divide both sides by $-2$.

$$x=\frac{-12}{-2}$$

Divide $-12$ by $-2$ to get $6$.

$$x=6$$