Solve 2*(x+4)-3*(x+1)^2=x*(6-3x)

$$2 \cdot ( x + 4 ) - 3 \cdot ( x + 1 ) ^ { 2 } = x \cdot ( 6 - 3 x )$$

Solve for x

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

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by x+4.

$$2x+8-3\left(x+1\right)^{2}=x\left(6-3x\right)$$

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

$$2x+8-3\left(x^{2}+2x+1\right)=x\left(6-3x\right)$$

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

$$2x+8-3x^{2}-6x-3=x\left(6-3x\right)$$

Combine 2x and -6x to get -4x.

$$-4x+8-3x^{2}-3=x\left(6-3x\right)$$

Subtract 3 from 8 to get 5.

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

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

$$-4x+5-3x^{2}=6x-3x^{2}$$

Subtract 6x from both sides.

$$-4x+5-3x^{2}-6x=-3x^{2}$$

Combine -4x and -6x to get -10x.

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

Add 3x^{2} to both sides.

$$-10x+5-3x^{2}+3x^{2}=0$$

Combine -3x^{2} and 3x^{2} to get 0.

$$-10x+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-10x=-5$$

Divide both sides by -10.

$$x=\frac{-5}{-10}$$

Reduce the fraction \frac{-5}{-10} to lowest terms by extracting and canceling out -5.

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