Solve (2x-6)(8x-3)-(3+4x)(4x-7)=0

$$(2x-6)(8x-3)-(3+4x)(4x-7)=0$$

Solve for x

$$x = \frac{39}{38} = 1\frac{1}{38} \approx 1.026315789$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x-6 by 8x-3 and combine like terms.

$$16x^{2}-54x+18-\left(3+4x\right)\left(4x-7\right)=0$$

Use the distributive property to multiply 3+4x by 4x-7 and combine like terms.

$$16x^{2}-54x+18-\left(-16x-21+16x^{2}\right)=0$$

To find the opposite of -16x-21+16x^{2}, find the opposite of each term.

$$16x^{2}-54x+18+16x+21-16x^{2}=0$$

Combine -54x and 16x to get -38x.

$$16x^{2}-38x+18+21-16x^{2}=0$$

Add 18 and 21 to get 39.

$$16x^{2}-38x+39-16x^{2}=0$$

Combine 16x^{2} and -16x^{2} to get 0.

$$-38x+39=0$$

Subtract 39 from both sides. Anything subtracted from zero gives its negation.

$$-38x=-39$$

Divide both sides by -38.

$$x=\frac{-39}{-38}$$

Fraction \frac{-39}{-38} can be simplified to \frac{39}{38} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{39}{38}$$