Solve 6(3-2t)=1+4(5-3i)

$$6 ( 3 - 2 t ) = 1 + 4 ( 5 - 3 i )$$

Solve for t

$$t=-\frac{1}{4}+i=-0.25+i$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6 by 3-2t.

$$18-12t=1+4\left(5-3i\right)$$

Multiply 4 times 5-3i.

$$18-12t=1+4\times 5+4\times \left(-3i\right)$$

Do the multiplications in 4\times 5+4\times \left(-3i\right).

$$18-12t=1+\left(20-12i\right)$$

Combine the real and imaginary parts in 1+20-12i.

$$18-12t=1+20-12i$$

Add 1 to 20.

$$18-12t=21-12i$$

Subtract 18 from both sides.

$$-12t=21-12i-18$$

Subtract 18 from 21-12i by subtracting corresponding real and imaginary parts.

$$-12t=21-18-12i$$

Subtract 18 from 21 to get 3.

$$-12t=3-12i$$

Divide both sides by -12.

$$t=\frac{3-12i}{-12}$$

Divide 3-12i by -12 to get -\frac{1}{4}+i.

$$t=-\frac{1}{4}+i$$