Solve 14-(5x-1)(2x+3)=17-(10x-1)(x-6)

$$14 - ( 5 x - 1 ) ( 2 x + 3 ) = 17 - ( 10 x - 1 ) ( x - 6 )$$

Solve for x

$$x=\frac{3}{37}\approx 0.081081081$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5x-1 by 2x+3 and combine like terms.

$$14-\left(10x^{2}+13x-3\right)=17-\left(10x-1\right)\left(x-6\right)$$

To find the opposite of 10x^{2}+13x-3, find the opposite of each term.

$$14-10x^{2}-13x+3=17-\left(10x-1\right)\left(x-6\right)$$

Add 14 and 3 to get 17.

$$17-10x^{2}-13x=17-\left(10x-1\right)\left(x-6\right)$$

Use the distributive property to multiply 10x-1 by x-6 and combine like terms.

$$17-10x^{2}-13x=17-\left(10x^{2}-61x+6\right)$$

To find the opposite of 10x^{2}-61x+6, find the opposite of each term.

$$17-10x^{2}-13x=17-10x^{2}+61x-6$$

Subtract 6 from 17 to get 11.

$$17-10x^{2}-13x=11-10x^{2}+61x$$

Add 10x^{2} to both sides.

$$17-10x^{2}-13x+10x^{2}=11+61x$$

Combine -10x^{2} and 10x^{2} to get 0.

$$17-13x=11+61x$$

Subtract 61x from both sides.

$$17-13x-61x=11$$

Combine -13x and -61x to get -74x.

$$17-74x=11$$

Subtract 17 from both sides.

$$-74x=11-17$$

Subtract 17 from 11 to get -6.

$$-74x=-6$$

Divide both sides by -74.

$$x=\frac{-6}{-74}$$

Reduce the fraction \frac{-6}{-74} to lowest terms by extracting and canceling out -2.

$$x=\frac{3}{37}$$