Solve left(2x+1right)^2/5-left(x-1right)^2/3=7x^2-14x-5/15

$$\frac{ { \left(2x+1 \right) }^{ 2 } }{ 5 } - \frac{ { \left(x-1 \right) }^{ 2 } }{ 3 } = \frac{ 7 { x }^{ 2 } -14x-5 }{ 15 }$$

Solve for x

$$x=-\frac{1}{12}\approx -0.083333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3,15.

$$3\left(2x+1\right)^{2}-5\left(x-1\right)^{2}=7x^{2}-14x-5$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$3\left(4x^{2}+4x+1\right)-5\left(x-1\right)^{2}=7x^{2}-14x-5$$

Use the distributive property to multiply 3 by 4x^{2}+4x+1.

$$12x^{2}+12x+3-5\left(x-1\right)^{2}=7x^{2}-14x-5$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$12x^{2}+12x+3-5\left(x^{2}-2x+1\right)=7x^{2}-14x-5$$

Use the distributive property to multiply -5 by x^{2}-2x+1.

$$12x^{2}+12x+3-5x^{2}+10x-5=7x^{2}-14x-5$$

Combine 12x^{2} and -5x^{2} to get 7x^{2}.

$$7x^{2}+12x+3+10x-5=7x^{2}-14x-5$$

Combine 12x and 10x to get 22x.

$$7x^{2}+22x+3-5=7x^{2}-14x-5$$

Subtract 5 from 3 to get -2.

$$7x^{2}+22x-2=7x^{2}-14x-5$$

Subtract 7x^{2} from both sides.

$$7x^{2}+22x-2-7x^{2}=-14x-5$$

Combine 7x^{2} and -7x^{2} to get 0.

$$22x-2=-14x-5$$

Add 14x to both sides.

$$22x-2+14x=-5$$

Combine 22x and 14x to get 36x.

$$36x-2=-5$$

Add 2 to both sides.

$$36x=-5+2$$

Add -5 and 2 to get -3.

$$36x=-3$$

Divide both sides by 36.

$$x=\frac{-3}{36}$$

Reduce the fraction \frac{-3}{36} to lowest terms by extracting and canceling out 3.

$$x=-\frac{1}{12}$$