(5t-8)(5t-8)-9(5t-8)+14=0

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Solution for (5t-8)(5t-8)-9(5t-8)+14=0 equation: 


Simplifying
(5t + -8)(5t + -8) + -9(5t + -8) + 14 = 0

Reorder the terms:
(-8 + 5t)(5t + -8) + -9(5t + -8) + 14 = 0

Reorder the terms:
(-8 + 5t)(-8 + 5t) + -9(5t + -8) + 14 = 0

Multiply (-8 + 5t) * (-8 + 5t)
(-8(-8 + 5t) + 5t * (-8 + 5t)) + -9(5t + -8) + 14 = 0
((-8 * -8 + 5t * -8) + 5t * (-8 + 5t)) + -9(5t + -8) + 14 = 0
((64 + -40t) + 5t * (-8 + 5t)) + -9(5t + -8) + 14 = 0
(64 + -40t + (-8 * 5t + 5t * 5t)) + -9(5t + -8) + 14 = 0
(64 + -40t + (-40t + 25t2)) + -9(5t + -8) + 14 = 0

Combine like terms: -40t + -40t = -80t
(64 + -80t + 25t2) + -9(5t + -8) + 14 = 0

Reorder the terms:
64 + -80t + 25t2 + -9(-8 + 5t) + 14 = 0
64 + -80t + 25t2 + (-8 * -9 + 5t * -9) + 14 = 0
64 + -80t + 25t2 + (72 + -45t) + 14 = 0

Reorder the terms:
64 + 72 + 14 + -80t + -45t + 25t2 = 0

Combine like terms: 64 + 72 = 136
136 + 14 + -80t + -45t + 25t2 = 0

Combine like terms: 136 + 14 = 150
150 + -80t + -45t + 25t2 = 0

Combine like terms: -80t + -45t = -125t
150 + -125t + 25t2 = 0

Solving
150 + -125t + 25t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '25'.
25(6 + -5t + t2) = 0

Factor a trinomial.
25((2 + -1t)(3 + -1t)) = 0

Ignore the factor 25.

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {2, 3}

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