0=-4(4t^2-16t+7)

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Solution for 0=-4(4t^2-16t+7) equation:


Simplifying
0 = -4(4t2 + -16t + 7)

Reorder the terms:
0 = -4(7 + -16t + 4t2)
0 = (7 * -4 + -16t * -4 + 4t2 * -4)
0 = (-28 + 64t + -16t2)

Solving
0 = -28 + 64t + -16t2

Solving for variable 't'.

Combine like terms: 0 + 28 = 28
28 + -64t + 16t2 = -28 + 64t + -16t2 + 28 + -64t + 16t2

Reorder the terms:
28 + -64t + 16t2 = -28 + 28 + 64t + -64t + -16t2 + 16t2

Combine like terms: -28 + 28 = 0
28 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2
28 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2

Combine like terms: 64t + -64t = 0
28 + -64t + 16t2 = 0 + -16t2 + 16t2
28 + -64t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
28 + -64t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -16t + 4t2) = 0

Factor a trinomial.
4((1 + -2t)(7 + -2t)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5

Subproblem 2

Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5

Solution

t = {0.5, 3.5}

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