9t+5(t+3)=t(t+13)+t

Solution for 9t+5(t+3)=t(t+13)+t equation:

Simplifying
9t + 5(t + 3) = t(t + 13) + t

Reorder the terms:
9t + 5(3 + t) = t(t + 13) + t
9t + (3 * 5 + t * 5) = t(t + 13) + t
9t + (15 + 5t) = t(t + 13) + t

Reorder the terms:
15 + 9t + 5t = t(t + 13) + t

Combine like terms: 9t + 5t = 14t
15 + 14t = t(t + 13) + t

Reorder the terms:
15 + 14t = t(13 + t) + t
15 + 14t = (13 * t + t * t) + t
15 + 14t = (13t + t2) + t

Reorder the terms:
15 + 14t = 13t + t + t2

Combine like terms: 13t + t = 14t
15 + 14t = 14t + t2

Add '-14t' to each side of the equation.
15 + 14t + -14t = 14t + -14t + t2

Combine like terms: 14t + -14t = 0
15 + 0 = 14t + -14t + t2
15 = 14t + -14t + t2

Combine like terms: 14t + -14t = 0
15 = 0 + t2
15 = t2

Solving
15 = t2

Solving for variable 't'.

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

Add '-1t2' to each side of the equation.
15 + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
15 + -1t2 = 0

Add '-15' to each side of the equation.
15 + -15 + -1t2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1t2 = 0 + -15
-1t2 = 0 + -15

Combine like terms: 0 + -15 = -15
-1t2 = -15

Divide each side by '-1'.
t2 = 15

Simplifying
t2 = 15

Take the square root of each side:
t = {-3.872983346, 3.872983346}