Solve A=(8x-3)(8x+1)-(2x-9)(-5+4x)

$$A = ( 8 x - 3 ) ( 8 x + 1 ) - ( 2 x - 9 ) ( - 5 + 4 x )$$

Solve for A

$$A=56x^{2}+30x-48$$

Solution Steps

Use the distributive property to multiply 8x-3 by 8x+1 and combine like terms.

$$A=64x^{2}-16x-3-\left(2x-9\right)\left(-5+4x\right)$$

Use the distributive property to multiply 2x-9 by -5+4x and combine like terms.

$$A=64x^{2}-16x-3-\left(-46x+8x^{2}+45\right)$$

To find the opposite of -46x+8x^{2}+45, find the opposite of each term.

$$A=64x^{2}-16x-3+46x-8x^{2}-45$$

Combine -16x and 46x to get 30x.

$$A=64x^{2}+30x-3-8x^{2}-45$$

Combine 64x^{2} and -8x^{2} to get 56x^{2}.

$$A=56x^{2}+30x-3-45$$

Subtract 45 from -3 to get -48.

$$A=56x^{2}+30x-48$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{56A+2913}-15}{56}$$

$$x=\frac{\sqrt{56A+2913}-15}{56}$$

Solve for x

$$x=\frac{-\sqrt{56A+2913}-15}{56}$$

$$x=\frac{\sqrt{56A+2913}-15}{56}\text{, }A\geq -\frac{2913}{56}$$