=7t(t-4)-2t(8t^2-4t+3)

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Solution for =7t(t-4)-2t(8t^2-4t+3) equation: 


Simplifying
0 = 7t(t + -4) + -2t(8t2 + -4t + 3)

Reorder the terms:
0 = 7t(-4 + t) + -2t(8t2 + -4t + 3)
0 = (-4 * 7t + t * 7t) + -2t(8t2 + -4t + 3)
0 = (-28t + 7t2) + -2t(8t2 + -4t + 3)

Reorder the terms:
0 = -28t + 7t2 + -2t(3 + -4t + 8t2)
0 = -28t + 7t2 + (3 * -2t + -4t * -2t + 8t2 * -2t)
0 = -28t + 7t2 + (-6t + 8t2 + -16t3)

Reorder the terms:
0 = -28t + -6t + 7t2 + 8t2 + -16t3

Combine like terms: -28t + -6t = -34t
0 = -34t + 7t2 + 8t2 + -16t3

Combine like terms: 7t2 + 8t2 = 15t2
0 = -34t + 15t2 + -16t3

Solving
0 = -34t + 15t2 + -16t3

Solving for variable 't'.
Remove the zero:
34t + -15t2 + 16t3 = -34t + 15t2 + -16t3 + 34t + -15t2 + 16t3

Reorder the terms:
34t + -15t2 + 16t3 = -34t + 34t + 15t2 + -15t2 + -16t3 + 16t3

Combine like terms: -34t + 34t = 0
34t + -15t2 + 16t3 = 0 + 15t2 + -15t2 + -16t3 + 16t3
34t + -15t2 + 16t3 = 15t2 + -15t2 + -16t3 + 16t3

Combine like terms: 15t2 + -15t2 = 0
34t + -15t2 + 16t3 = 0 + -16t3 + 16t3
34t + -15t2 + 16t3 = -16t3 + 16t3

Combine like terms: -16t3 + 16t3 = 0
34t + -15t2 + 16t3 = 0

Factor out the Greatest Common Factor (GCF), 't'.
t(34 + -15t + 16t2) = 0


Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Simplifying
t = 0

Subproblem 2
Set the factor '(34 + -15t + 16t2)' equal to zero and attempt to solve:

Simplifying
34 + -15t + 16t2 = 0

Solving
34 + -15t + 16t2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
2.125 + -0.9375t + t2 = 0

Move the constant term to the right:

Add '-2.125' to each side of the equation.
2.125 + -0.9375t + -2.125 + t2 = 0 + -2.125

Reorder the terms:
2.125 + -2.125 + -0.9375t + t2 = 0 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + -0.9375t + t2 = 0 + -2.125
-0.9375t + t2 = 0 + -2.125

Combine like terms: 0 + -2.125 = -2.125
-0.9375t + t2 = -2.125

The t term is -0.9375t.  Take half its coefficient (-0.46875).
Square it (0.2197265625) and add it to both sides.

Add '0.2197265625' to each side of the equation.
-0.9375t + 0.2197265625 + t2 = -2.125 + 0.2197265625

Reorder the terms:
0.2197265625 + -0.9375t + t2 = -2.125 + 0.2197265625

Combine like terms: -2.125 + 0.2197265625 = -1.9052734375
0.2197265625 + -0.9375t + t2 = -1.9052734375

Factor a perfect square on the left side:
(t + -0.46875)(t + -0.46875) = -1.9052734375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
t = {0}

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