Solve 5-2t-3/3=left(t+1right)^2-3t^2+1/3

$$5- \frac{ 2t-3 }{ 3 } = { \left(t+1 \right) }^{ 2 } - \frac{ 3 { t }^{ 2 } +1 }{ 3 }$$

Solve for t

$$t=2$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

$$15-\left(2t-3\right)=3\left(t+1\right)^{2}-\left(3t^{2}+1\right)$$

To find the opposite of 2t-3, find the opposite of each term.

$$15-2t+3=3\left(t+1\right)^{2}-\left(3t^{2}+1\right)$$

Add 15 and 3 to get 18.

$$18-2t=3\left(t+1\right)^{2}-\left(3t^{2}+1\right)$$

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

$$18-2t=3\left(t^{2}+2t+1\right)-\left(3t^{2}+1\right)$$

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

$$18-2t=3t^{2}+6t+3-\left(3t^{2}+1\right)$$

To find the opposite of 3t^{2}+1, find the opposite of each term.

$$18-2t=3t^{2}+6t+3-3t^{2}-1$$

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

$$18-2t=6t+3-1$$

Subtract 1 from 3 to get 2.

$$18-2t=6t+2$$

Subtract 6t from both sides.

$$18-2t-6t=2$$

Combine -2t and -6t to get -8t.

$$18-8t=2$$

Subtract 18 from both sides.

$$-8t=2-18$$

Subtract 18 from 2 to get -16.

$$-8t=-16$$

Divide both sides by -8.

$$t=\frac{-16}{-8}$$

Divide -16 by -8 to get 2.

$$t=2$$