Solve A=(x-2)(3x-5)+(3x-5)(3x+5) | 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

$$A=(x-2)(3x-5)+(3x-5)(3x+5)$$

Solve for A

$A=\left(3x-5\right)\left(4x+3\right)$

Solution Steps

Use the distributive property to multiply $x-2$ by $3x-5$ and combine like terms.

$$A=3x^{2}-11x+10+\left(3x-5\right)\left(3x+5\right)$$

Consider $\left(3x-5\right)\left(3x+5\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$. Square $5$.

$$A=3x^{2}-11x+10+\left(3x\right)^{2}-25$$

Expand $\left(3x\right)^{2}$.

$$A=3x^{2}-11x+10+3^{2}x^{2}-25$$

Calculate $3$ to the power of $2$ and get $9$.

$$A=3x^{2}-11x+10+9x^{2}-25$$

Combine $3x^{2}$ and $9x^{2}$ to get $12x^{2}$.

$$A=12x^{2}-11x+10-25$$

Subtract $25$ from $10$ to get $-15$.

$$A=12x^{2}-11x-15$$

Solve for x (complex solution)

$x=\frac{-\sqrt{48A+841}+11}{24}$
$x=\frac{\sqrt{48A+841}+11}{24}$

Solve for x

$x=\frac{-\sqrt{48A+841}+11}{24}$
$x=\frac{\sqrt{48A+841}+11}{24}\text{, }A\geq -\frac{841}{48}$