2w-3+3w(w-4)-5(w-6)=

Solution for 2w-3+3w(w-4)-5(w-6)= equation:

Simplifying
2w + -3 + 3w(w + -4) + -5(w + -6) = 0

Reorder the terms:
2w + -3 + 3w(-4 + w) + -5(w + -6) = 0
2w + -3 + (-4 * 3w + w * 3w) + -5(w + -6) = 0
2w + -3 + (-12w + 3w2) + -5(w + -6) = 0

Reorder the terms:
2w + -3 + -12w + 3w2 + -5(-6 + w) = 0
2w + -3 + -12w + 3w2 + (-6 * -5 + w * -5) = 0
2w + -3 + -12w + 3w2 + (30 + -5w) = 0

Reorder the terms:
-3 + 30 + 2w + -12w + -5w + 3w2 = 0

Combine like terms: -3 + 30 = 27
27 + 2w + -12w + -5w + 3w2 = 0

Combine like terms: 2w + -12w = -10w
27 + -10w + -5w + 3w2 = 0

Combine like terms: -10w + -5w = -15w
27 + -15w + 3w2 = 0

Solving
27 + -15w + 3w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(9 + -5w + w2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(9 + -5w + w2)' equal to zero and attempt to solve:

Simplifying
9 + -5w + w2 = 0

Solving
9 + -5w + w2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -5w + -9 + w2 = 0 + -9

Reorder the terms:
9 + -9 + -5w + w2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5w + w2 = 0 + -9
-5w + w2 = 0 + -9

Combine like terms: 0 + -9 = -9
-5w + w2 = -9

The w term is -5w.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5w + 6.25 + w2 = -9 + 6.25

Reorder the terms:
6.25 + -5w + w2 = -9 + 6.25

Combine like terms: -9 + 6.25 = -2.75
6.25 + -5w + w2 = -2.75

Factor a perfect square on the left side:
(w + -2.5)(w + -2.5) = -2.75

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.

The solution to this equation could not be determined.