(3t-2)(9t+4)=(9t-5)(3t+5)

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Solution for (3t-2)(9t+4)=(9t-5)(3t+5) equation: 


Simplifying
(3t + -2)(9t + 4) = (9t + -5)(3t + 5)

Reorder the terms:
(-2 + 3t)(9t + 4) = (9t + -5)(3t + 5)

Reorder the terms:
(-2 + 3t)(4 + 9t) = (9t + -5)(3t + 5)

Multiply (-2 + 3t) * (4 + 9t)
(-2(4 + 9t) + 3t * (4 + 9t)) = (9t + -5)(3t + 5)
((4 * -2 + 9t * -2) + 3t * (4 + 9t)) = (9t + -5)(3t + 5)
((-8 + -18t) + 3t * (4 + 9t)) = (9t + -5)(3t + 5)
(-8 + -18t + (4 * 3t + 9t * 3t)) = (9t + -5)(3t + 5)
(-8 + -18t + (12t + 27t2)) = (9t + -5)(3t + 5)

Combine like terms: -18t + 12t = -6t
(-8 + -6t + 27t2) = (9t + -5)(3t + 5)

Reorder the terms:
-8 + -6t + 27t2 = (-5 + 9t)(3t + 5)

Reorder the terms:
-8 + -6t + 27t2 = (-5 + 9t)(5 + 3t)

Multiply (-5 + 9t) * (5 + 3t)
-8 + -6t + 27t2 = (-5(5 + 3t) + 9t * (5 + 3t))
-8 + -6t + 27t2 = ((5 * -5 + 3t * -5) + 9t * (5 + 3t))
-8 + -6t + 27t2 = ((-25 + -15t) + 9t * (5 + 3t))
-8 + -6t + 27t2 = (-25 + -15t + (5 * 9t + 3t * 9t))
-8 + -6t + 27t2 = (-25 + -15t + (45t + 27t2))

Combine like terms: -15t + 45t = 30t
-8 + -6t + 27t2 = (-25 + 30t + 27t2)

Add '-27t2' to each side of the equation.
-8 + -6t + 27t2 + -27t2 = -25 + 30t + 27t2 + -27t2

Combine like terms: 27t2 + -27t2 = 0
-8 + -6t + 0 = -25 + 30t + 27t2 + -27t2
-8 + -6t = -25 + 30t + 27t2 + -27t2

Combine like terms: 27t2 + -27t2 = 0
-8 + -6t = -25 + 30t + 0
-8 + -6t = -25 + 30t

Solving
-8 + -6t = -25 + 30t

Solving for variable 't'.

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

Add '-30t' to each side of the equation.
-8 + -6t + -30t = -25 + 30t + -30t

Combine like terms: -6t + -30t = -36t
-8 + -36t = -25 + 30t + -30t

Combine like terms: 30t + -30t = 0
-8 + -36t = -25 + 0
-8 + -36t = -25

Add '8' to each side of the equation.
-8 + 8 + -36t = -25 + 8

Combine like terms: -8 + 8 = 0
0 + -36t = -25 + 8
-36t = -25 + 8

Combine like terms: -25 + 8 = -17
-36t = -17

Divide each side by '-36'.
t = 0.4722222222

Simplifying
t = 0.4722222222

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