Solve 3(2x+1)(-x+3)-(2x+5)^2=-[-(-3(x+5))+10x^2]

$$3 ( 2 x + 1 ) ( - x + 3 ) - ( 2 x + 5 ) ^ { 2 } = - [ - ( - 3 ( x + 5 ) ) + 10 x ^ { 2 } ]$$

Solve for x

$$x=-\frac{1}{2}=-0.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2x+1.

$$\left(6x+3\right)\left(-x+3\right)-\left(2x+5\right)^{2}=-\left(-\left(-3\left(x+5\right)\right)+10x^{2}\right)$$

Use the distributive property to multiply 6x+3 by -x+3.

$$6x\left(-x\right)+18x+3\left(-x\right)+9-\left(2x+5\right)^{2}=-\left(-\left(-3\left(x+5\right)\right)+10x^{2}\right)$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+5\right)^{2}.

$$6x\left(-x\right)+18x+3\left(-x\right)+9-\left(4x^{2}+20x+25\right)=-\left(-\left(-3\left(x+5\right)\right)+10x^{2}\right)$$

To find the opposite of 4x^{2}+20x+25, find the opposite of each term.

$$6x\left(-x\right)+18x+3\left(-x\right)+9-4x^{2}-20x-25=-\left(-\left(-3\left(x+5\right)\right)+10x^{2}\right)$$

Combine 18x and -20x to get -2x.

$$6x\left(-x\right)-2x+3\left(-x\right)+9-4x^{2}-25=-\left(-\left(-3\left(x+5\right)\right)+10x^{2}\right)$$

Subtract 25 from 9 to get -16.

$$6x\left(-x\right)-2x+3\left(-x\right)-16-4x^{2}=-\left(-\left(-3\left(x+5\right)\right)+10x^{2}\right)$$

Use the distributive property to multiply -3 by x+5.

$$6x\left(-x\right)-2x+3\left(-x\right)-16-4x^{2}=-\left(-\left(-3x-15\right)+10x^{2}\right)$$

To find the opposite of -3x-15, find the opposite of each term.

$$6x\left(-x\right)-2x+3\left(-x\right)-16-4x^{2}=-\left(3x+15+10x^{2}\right)$$

To find the opposite of 3x+15+10x^{2}, find the opposite of each term.

$$6x\left(-x\right)-2x+3\left(-x\right)-16-4x^{2}=-3x-15-10x^{2}$$

Add 3x to both sides.

$$6x\left(-x\right)-2x+3\left(-x\right)-16-4x^{2}+3x=-15-10x^{2}$$

Combine -2x and 3x to get x.

$$6x\left(-x\right)+x+3\left(-x\right)-16-4x^{2}=-15-10x^{2}$$

Add 10x^{2} to both sides.

$$6x\left(-x\right)+x+3\left(-x\right)-16-4x^{2}+10x^{2}=-15$$

Combine -4x^{2} and 10x^{2} to get 6x^{2}.

$$6x\left(-x\right)+x+3\left(-x\right)-16+6x^{2}=-15$$

Add 16 to both sides.

$$6x\left(-x\right)+x+3\left(-x\right)+6x^{2}=-15+16$$

Add -15 and 16 to get 1.

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

Multiply 6 and -1 to get -6.

$$-6xx+x+3\left(-1\right)x+6x^{2}=1$$

Multiply x and x to get x^{2}.

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

Multiply 3 and -1 to get -3.

$$-6x^{2}+x-3x+6x^{2}=1$$

Combine x and -3x to get -2x.

$$-6x^{2}-2x+6x^{2}=1$$

Combine -6x^{2} and 6x^{2} to get 0.

$$-2x=1$$

Divide both sides by -2.

$$x=\frac{1}{-2}$$

Fraction \frac{1}{-2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x=-\frac{1}{2}$$