Solve 10x-7/15x+3=3x+8/12-5x^2-4/20x+4

$$\frac { 10 x - 7 } { 15 x + 3 } = \frac { 3 x + 8 } { 12 } - \frac { 5 x ^ { 2 } - 4 } { 20 x + 4 }$$

Solve for x

$$x=-16$$

Steps for Solving Linear Equation

Variable x cannot be equal to -\frac{1}{5} since division by zero is not defined. Multiply both sides of the equation by 12\left(5x+1\right), the least common multiple of 15x+3,12,20x+4.

$$4\left(10x-7\right)=\left(5x+1\right)\left(3x+8\right)-3\left(5x^{2}-4\right)$$

Use the distributive property to multiply 4 by 10x-7.

$$40x-28=\left(5x+1\right)\left(3x+8\right)-3\left(5x^{2}-4\right)$$

Use the distributive property to multiply 5x+1 by 3x+8 and combine like terms.

$$40x-28=15x^{2}+43x+8-3\left(5x^{2}-4\right)$$

Use the distributive property to multiply -3 by 5x^{2}-4.

$$40x-28=15x^{2}+43x+8-15x^{2}+12$$

Combine 15x^{2} and -15x^{2} to get 0.

$$40x-28=43x+8+12$$

Add 8 and 12 to get 20.

$$40x-28=43x+20$$

Subtract 43x from both sides.

$$40x-28-43x=20$$

Combine 40x and -43x to get -3x.

$$-3x-28=20$$

Add 28 to both sides.

$$-3x=20+28$$

Add 20 and 28 to get 48.

$$-3x=48$$

Divide both sides by -3.

$$x=\frac{48}{-3}$$

Divide 48 by -3 to get -16.

$$x=-16$$