(2w+4)(w-3)=600

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Solution for (2w+4)(w-3)=600 equation: 


Simplifying
(2w + 4)(w + -3) = 600

Reorder the terms:
(4 + 2w)(w + -3) = 600

Reorder the terms:
(4 + 2w)(-3 + w) = 600

Multiply (4 + 2w) * (-3 + w)
(4(-3 + w) + 2w * (-3 + w)) = 600
((-3 * 4 + w * 4) + 2w * (-3 + w)) = 600
((-12 + 4w) + 2w * (-3 + w)) = 600
(-12 + 4w + (-3 * 2w + w * 2w)) = 600
(-12 + 4w + (-6w + 2w2)) = 600

Combine like terms: 4w + -6w = -2w
(-12 + -2w + 2w2) = 600

Solving
-12 + -2w + 2w2 = 600

Solving for variable 'w'.

Reorder the terms:
-12 + -600 + -2w + 2w2 = 600 + -600

Combine like terms: -12 + -600 = -612
-612 + -2w + 2w2 = 600 + -600

Combine like terms: 600 + -600 = 0
-612 + -2w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-306 + -1w + w2) = 0

Factor a trinomial.
2((-17 + -1w)(18 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + -1w)' equal to zero and attempt to solve:

Simplifying
-17 + -1w = 0

Solving
-17 + -1w = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1w = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1w = 0 + 17
-1w = 0 + 17

Combine like terms: 0 + 17 = 17
-1w = 17

Divide each side by '-1'.
w = -17

Simplifying
w = -17

Subproblem 2
Set the factor '(18 + -1w)' equal to zero and attempt to solve:

Simplifying
18 + -1w = 0

Solving
18 + -1w = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1w = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1w = 0 + -18
-1w = 0 + -18

Combine like terms: 0 + -18 = -18
-1w = -18

Divide each side by '-1'.
w = 18

Simplifying
w = 18
Solution
w = {-17, 18}

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