3t(t-5)+14=5-t(t+3)

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Solution for 3t(t-5)+14=5-t(t+3) equation: 


Simplifying
3t(t + -5) + 14 = 5 + -1t(t + 3)

Reorder the terms:
3t(-5 + t) + 14 = 5 + -1t(t + 3)
(-5 * 3t + t * 3t) + 14 = 5 + -1t(t + 3)
(-15t + 3t2) + 14 = 5 + -1t(t + 3)

Reorder the terms:
14 + -15t + 3t2 = 5 + -1t(t + 3)

Reorder the terms:
14 + -15t + 3t2 = 5 + -1t(3 + t)
14 + -15t + 3t2 = 5 + (3 * -1t + t * -1t)
14 + -15t + 3t2 = 5 + (-3t + -1t2)

Solving
14 + -15t + 3t2 = 5 + -3t + -1t2

Solving for variable 't'.

Reorder the terms:
14 + -5 + -15t + 3t + 3t2 + t2 = 5 + -3t + -1t2 + -5 + 3t + t2

Combine like terms: 14 + -5 = 9
9 + -15t + 3t + 3t2 + t2 = 5 + -3t + -1t2 + -5 + 3t + t2

Combine like terms: -15t + 3t = -12t
9 + -12t + 3t2 + t2 = 5 + -3t + -1t2 + -5 + 3t + t2

Combine like terms: 3t2 + t2 = 4t2
9 + -12t + 4t2 = 5 + -3t + -1t2 + -5 + 3t + t2

Reorder the terms:
9 + -12t + 4t2 = 5 + -5 + -3t + 3t + -1t2 + t2

Combine like terms: 5 + -5 = 0
9 + -12t + 4t2 = 0 + -3t + 3t + -1t2 + t2
9 + -12t + 4t2 = -3t + 3t + -1t2 + t2

Combine like terms: -3t + 3t = 0
9 + -12t + 4t2 = 0 + -1t2 + t2
9 + -12t + 4t2 = -1t2 + t2

Combine like terms: -1t2 + t2 = 0
9 + -12t + 4t2 = 0

Factor a trinomial.
(3 + -2t)(3 + -2t) = 0


Subproblem 1
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5

Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve:

Simplifying
3 + -2t = 0

Solving
3 + -2t = 0

Move all terms containing t to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2t = 0 + -3
-2t = 0 + -3

Combine like terms: 0 + -3 = -3
-2t = -3

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {1.5, 1.5}

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