Solve 4(a+3)(2a-1)=2(4a^2+8a-3)

$$4 ( a + 3 ) ( 2 a - 1 ) = 2 ( 4 a ^ { 2 } + 8 a - 3 )$$

Solve for a

$$a = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by a+3.

$$\left(4a+12\right)\left(2a-1\right)=2\left(4a^{2}+8a-3\right)$$

Use the distributive property to multiply 4a+12 by 2a-1 and combine like terms.

$$8a^{2}+20a-12=2\left(4a^{2}+8a-3\right)$$

Use the distributive property to multiply 2 by 4a^{2}+8a-3.

$$8a^{2}+20a-12=8a^{2}+16a-6$$

Subtract 8a^{2} from both sides.

$$8a^{2}+20a-12-8a^{2}=16a-6$$

Combine 8a^{2} and -8a^{2} to get 0.

$$20a-12=16a-6$$

Subtract 16a from both sides.

$$20a-12-16a=-6$$

Combine 20a and -16a to get 4a.

$$4a-12=-6$$

Add 12 to both sides.

$$4a=-6+12$$

Add -6 and 12 to get 6.

$$4a=6$$

Divide both sides by 4.

$$a=\frac{6}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$a=\frac{3}{2}$$