Solve 12-x(2x+1)=3x-2x^2+7

$$12-x(2x+1)=3x-2 { x }^{ 2 } +7$$

Solve for x

$$x = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

Steps for Solving Linear Equation

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

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

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

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

Subtract 3x from both sides.

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

Combine -x and -3x to get -4x.

$$12-2x^{2}-4x=-2x^{2}+7$$

Add 2x^{2} to both sides.

$$12-2x^{2}-4x+2x^{2}=7$$

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

$$12-4x=7$$

Subtract 12 from both sides.

$$-4x=7-12$$

Subtract 12 from 7 to get -5.

$$-4x=-5$$

Divide both sides by -4.

$$x=\frac{-5}{-4}$$

Fraction \frac{-5}{-4} can be simplified to \frac{5}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{4}$$