Solve 1+-(5x-1)(2x+3)=17-(10x+4)(x-6)

$$1 + - ( 5 x - 1 ) ( 2 x + 3 ) = 17 - ( 10 x + 4 ) ( x - 6 )$$

Solve for x

$$x=-\frac{37}{69}\approx -0.536231884$$

Steps for Solving Linear Equation

To find the opposite of 5x-1, find the opposite of each term.

$$1+\left(-5x+1\right)\left(2x+3\right)=17-\left(10x+4\right)\left(x-6\right)$$

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

$$1-10x^{2}-13x+3=17-\left(10x+4\right)\left(x-6\right)$$

Add 1 and 3 to get 4.

$$4-10x^{2}-13x=17-\left(10x+4\right)\left(x-6\right)$$

Use the distributive property to multiply 10x+4 by x-6 and combine like terms.

$$4-10x^{2}-13x=17-\left(10x^{2}-56x-24\right)$$

To find the opposite of 10x^{2}-56x-24, find the opposite of each term.

$$4-10x^{2}-13x=17-10x^{2}+56x+24$$

Add 17 and 24 to get 41.

$$4-10x^{2}-13x=41-10x^{2}+56x$$

Add 10x^{2} to both sides.

$$4-10x^{2}-13x+10x^{2}=41+56x$$

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

$$4-13x=41+56x$$

Subtract 56x from both sides.

$$4-13x-56x=41$$

Combine -13x and -56x to get -69x.

$$4-69x=41$$

Subtract 4 from both sides.

$$-69x=41-4$$

Subtract 4 from 41 to get 37.

$$-69x=37$$

Divide both sides by -69.

$$x=\frac{37}{-69}$$

Fraction \frac{37}{-69} can be rewritten as -\frac{37}{69} by extracting the negative sign.

$$x=-\frac{37}{69}$$