(4w-3t)(4w+2t)=

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


Simplifying
(4w + -3t)(4w + 2t) = 0

Reorder the terms:
(-3t + 4w)(4w + 2t) = 0

Reorder the terms:
(-3t + 4w)(2t + 4w) = 0

Multiply (-3t + 4w) * (2t + 4w)
(-3t * (2t + 4w) + 4w * (2t + 4w)) = 0
((2t * -3t + 4w * -3t) + 4w * (2t + 4w)) = 0

Reorder the terms:
((-12tw + -6t2) + 4w * (2t + 4w)) = 0
((-12tw + -6t2) + 4w * (2t + 4w)) = 0
(-12tw + -6t2 + (2t * 4w + 4w * 4w)) = 0
(-12tw + -6t2 + (8tw + 16w2)) = 0

Reorder the terms:
(-12tw + 8tw + -6t2 + 16w2) = 0

Combine like terms: -12tw + 8tw = -4tw
(-4tw + -6t2 + 16w2) = 0

Solving
-4tw + -6t2 + 16w2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2tw + -3t2 + 8w2) = 0

Factor a trinomial.
2((-1t + -2w)(3t + -4w)) = 0

Ignore the factor 2.

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

Simplifying
-1t + -2w = 0

Solving
-1t + -2w = 0

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

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

Combine like terms: -2w + 2w = 0
-1t + 0 = 0 + 2w
-1t = 0 + 2w
Remove the zero:
-1t = 2w

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

Simplifying
t = -2w

Subproblem 2
Set the factor '(3t + -4w)' equal to zero and attempt to solve:

Simplifying
3t + -4w = 0

Solving
3t + -4w = 0

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

Add '4w' to each side of the equation.
3t + -4w + 4w = 0 + 4w

Combine like terms: -4w + 4w = 0
3t + 0 = 0 + 4w
3t = 0 + 4w
Remove the zero:
3t = 4w

Divide each side by '3'.
t = 1.333333333w

Simplifying
t = 1.333333333w
Solution
t = {-2w, 1.333333333w}

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