(3w+7)(4w-8)=

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Solution for (3w+7)(4w-8)= equation: 


Simplifying
(3w + 7)(4w + -8) = 0

Reorder the terms:
(7 + 3w)(4w + -8) = 0

Reorder the terms:
(7 + 3w)(-8 + 4w) = 0

Multiply (7 + 3w) * (-8 + 4w)
(7(-8 + 4w) + 3w * (-8 + 4w)) = 0
((-8 * 7 + 4w * 7) + 3w * (-8 + 4w)) = 0
((-56 + 28w) + 3w * (-8 + 4w)) = 0
(-56 + 28w + (-8 * 3w + 4w * 3w)) = 0
(-56 + 28w + (-24w + 12w2)) = 0

Combine like terms: 28w + -24w = 4w
(-56 + 4w + 12w2) = 0

Solving
-56 + 4w + 12w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + w + 3w2) = 0

Factor a trinomial.
4((-7 + -3w)(2 + -1w)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -3w)' equal to zero and attempt to solve:

Simplifying
-7 + -3w = 0

Solving
-7 + -3w = 0

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

Add '7' to each side of the equation.
-7 + 7 + -3w = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3w = 0 + 7
-3w = 0 + 7

Combine like terms: 0 + 7 = 7
-3w = 7

Divide each side by '-3'.
w = -2.333333333

Simplifying
w = -2.333333333

Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-2.333333333, 2}

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