(4t-7)(4t-7)-10(4t-7)+9=0

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Solution for (4t-7)(4t-7)-10(4t-7)+9=0 equation: 


Simplifying
(4t + -7)(4t + -7) + -10(4t + -7) + 9 = 0

Reorder the terms:
(-7 + 4t)(4t + -7) + -10(4t + -7) + 9 = 0

Reorder the terms:
(-7 + 4t)(-7 + 4t) + -10(4t + -7) + 9 = 0

Multiply (-7 + 4t) * (-7 + 4t)
(-7(-7 + 4t) + 4t * (-7 + 4t)) + -10(4t + -7) + 9 = 0
((-7 * -7 + 4t * -7) + 4t * (-7 + 4t)) + -10(4t + -7) + 9 = 0
((49 + -28t) + 4t * (-7 + 4t)) + -10(4t + -7) + 9 = 0
(49 + -28t + (-7 * 4t + 4t * 4t)) + -10(4t + -7) + 9 = 0
(49 + -28t + (-28t + 16t2)) + -10(4t + -7) + 9 = 0

Combine like terms: -28t + -28t = -56t
(49 + -56t + 16t2) + -10(4t + -7) + 9 = 0

Reorder the terms:
49 + -56t + 16t2 + -10(-7 + 4t) + 9 = 0
49 + -56t + 16t2 + (-7 * -10 + 4t * -10) + 9 = 0
49 + -56t + 16t2 + (70 + -40t) + 9 = 0

Reorder the terms:
49 + 70 + 9 + -56t + -40t + 16t2 = 0

Combine like terms: 49 + 70 = 119
119 + 9 + -56t + -40t + 16t2 = 0

Combine like terms: 119 + 9 = 128
128 + -56t + -40t + 16t2 = 0

Combine like terms: -56t + -40t = -96t
128 + -96t + 16t2 = 0

Solving
128 + -96t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '16'.
16(8 + -6t + t2) = 0

Factor a trinomial.
16((2 + -1t)(4 + -1t)) = 0

Ignore the factor 16.

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 '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {2, 4}

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