Solve (2x-5)(9x^2-4)=(18x^2-8)(x-8)

$$( 2 x - 5 ) ( 9 x ^ { 2 } - 4 ) = ( 18 x ^ { 2 } - 8 ) ( x - 8 )$$

Solve for x

$$x=-\frac{2}{3}\approx -0.666666667$$

$$x=\frac{2}{3}\approx 0.666666667$$

Steps Using Difference of Squares

Use the distributive property to multiply 2x-5 by 9x^{2}-4.

$$18x^{3}-8x-45x^{2}+20=\left(18x^{2}-8\right)\left(x-8\right)$$

Use the distributive property to multiply 18x^{2}-8 by x-8.

$$18x^{3}-8x-45x^{2}+20=18x^{3}-144x^{2}-8x+64$$

Subtract 18x^{3} from both sides.

$$18x^{3}-8x-45x^{2}+20-18x^{3}=-144x^{2}-8x+64$$

Combine 18x^{3} and -18x^{3} to get 0.

$$-8x-45x^{2}+20=-144x^{2}-8x+64$$

Add 144x^{2} to both sides.

$$-8x-45x^{2}+20+144x^{2}=-8x+64$$

Combine -45x^{2} and 144x^{2} to get 99x^{2}.

$$-8x+99x^{2}+20=-8x+64$$

Add 8x to both sides.

$$-8x+99x^{2}+20+8x=64$$

Combine -8x and 8x to get 0.

$$99x^{2}+20=64$$

Subtract 64 from both sides.

$$99x^{2}+20-64=0$$

Subtract 64 from 20 to get -44.

$$99x^{2}-44=0$$

Divide both sides by 11.

$$9x^{2}-4=0$$

Consider 9x^{2}-4. Rewrite 9x^{2}-4 as \left(3x\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(3x-2\right)\left(3x+2\right)=0$$

To find equation solutions, solve 3x-2=0 and 3x+2=0.

$$x=\frac{2}{3} x=-\frac{2}{3}$$

Steps by Finding Square Root

Use the distributive property to multiply 2x-5 by 9x^{2}-4.

$$18x^{3}-8x-45x^{2}+20=\left(18x^{2}-8\right)\left(x-8\right)$$

Use the distributive property to multiply 18x^{2}-8 by x-8.

$$18x^{3}-8x-45x^{2}+20=18x^{3}-144x^{2}-8x+64$$

Subtract 18x^{3} from both sides.

$$18x^{3}-8x-45x^{2}+20-18x^{3}=-144x^{2}-8x+64$$

Combine 18x^{3} and -18x^{3} to get 0.

$$-8x-45x^{2}+20=-144x^{2}-8x+64$$

Add 144x^{2} to both sides.

$$-8x-45x^{2}+20+144x^{2}=-8x+64$$

Combine -45x^{2} and 144x^{2} to get 99x^{2}.

$$-8x+99x^{2}+20=-8x+64$$

Add 8x to both sides.

$$-8x+99x^{2}+20+8x=64$$

Combine -8x and 8x to get 0.

$$99x^{2}+20=64$$

Subtract 20 from both sides.

$$99x^{2}=64-20$$

Subtract 20 from 64 to get 44.

$$99x^{2}=44$$

Divide both sides by 99.

$$x^{2}=\frac{44}{99}$$

Reduce the fraction \frac{44}{99} to lowest terms by extracting and canceling out 11.

$$x^{2}=\frac{4}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{2}{3} x=-\frac{2}{3}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x-5 by 9x^{2}-4.

$$18x^{3}-8x-45x^{2}+20=\left(18x^{2}-8\right)\left(x-8\right)$$

Use the distributive property to multiply 18x^{2}-8 by x-8.

$$18x^{3}-8x-45x^{2}+20=18x^{3}-144x^{2}-8x+64$$

Subtract 18x^{3} from both sides.

$$18x^{3}-8x-45x^{2}+20-18x^{3}=-144x^{2}-8x+64$$

Combine 18x^{3} and -18x^{3} to get 0.

$$-8x-45x^{2}+20=-144x^{2}-8x+64$$

Add 144x^{2} to both sides.

$$-8x-45x^{2}+20+144x^{2}=-8x+64$$

Combine -45x^{2} and 144x^{2} to get 99x^{2}.

$$-8x+99x^{2}+20=-8x+64$$

Add 8x to both sides.

$$-8x+99x^{2}+20+8x=64$$

Combine -8x and 8x to get 0.

$$99x^{2}+20=64$$

Subtract 64 from both sides.

$$99x^{2}+20-64=0$$

Subtract 64 from 20 to get -44.

$$99x^{2}-44=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 99 for a, 0 for b, and -44 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 99\left(-44\right)}}{2\times 99}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 99\left(-44\right)}}{2\times 99}$$

Multiply -4 times 99.

$$x=\frac{0±\sqrt{-396\left(-44\right)}}{2\times 99}$$

Multiply -396 times -44.

$$x=\frac{0±\sqrt{17424}}{2\times 99}$$

Take the square root of 17424.

$$x=\frac{0±132}{2\times 99}$$

Multiply 2 times 99.

$$x=\frac{0±132}{198}$$

Now solve the equation x=\frac{0±132}{198} when ± is plus. Reduce the fraction \frac{132}{198} to lowest terms by extracting and canceling out 66.

$$x=\frac{2}{3}$$

Now solve the equation x=\frac{0±132}{198} when ± is minus. Reduce the fraction \frac{-132}{198} to lowest terms by extracting and canceling out 66.

$$x=-\frac{2}{3}$$

The equation is now solved.

$$x=\frac{2}{3} x=-\frac{2}{3}$$