2(w+3)(w-1)-w(w+3)=150

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Solution for 2(w+3)(w-1)-w(w+3)=150 equation:


Simplifying
2(w + 3)(w + -1) + -1w(w + 3) = 150

Reorder the terms:
2(3 + w)(w + -1) + -1w(w + 3) = 150

Reorder the terms:
2(3 + w)(-1 + w) + -1w(w + 3) = 150

Multiply (3 + w) * (-1 + w)
2(3(-1 + w) + w(-1 + w)) + -1w(w + 3) = 150
2((-1 * 3 + w * 3) + w(-1 + w)) + -1w(w + 3) = 150
2((-3 + 3w) + w(-1 + w)) + -1w(w + 3) = 150
2(-3 + 3w + (-1 * w + w * w)) + -1w(w + 3) = 150
2(-3 + 3w + (-1w + w2)) + -1w(w + 3) = 150

Combine like terms: 3w + -1w = 2w
2(-3 + 2w + w2) + -1w(w + 3) = 150
(-3 * 2 + 2w * 2 + w2 * 2) + -1w(w + 3) = 150
(-6 + 4w + 2w2) + -1w(w + 3) = 150

Reorder the terms:
-6 + 4w + 2w2 + -1w(3 + w) = 150
-6 + 4w + 2w2 + (3 * -1w + w * -1w) = 150
-6 + 4w + 2w2 + (-3w + -1w2) = 150

Reorder the terms:
-6 + 4w + -3w + 2w2 + -1w2 = 150

Combine like terms: 4w + -3w = 1w
-6 + 1w + 2w2 + -1w2 = 150

Combine like terms: 2w2 + -1w2 = 1w2
-6 + 1w + 1w2 = 150

Solving
-6 + 1w + 1w2 = 150

Solving for variable 'w'.

Reorder the terms:
-6 + -150 + 1w + 1w2 = 150 + -150

Combine like terms: -6 + -150 = -156
-156 + 1w + 1w2 = 150 + -150

Combine like terms: 150 + -150 = 0
-156 + 1w + 1w2 = 0

Factor a trinomial.
(-13 + -1w)(12 + -1w) = 0

Subproblem 1

Set the factor '(-13 + -1w)' equal to zero and attempt to solve: Simplifying -13 + -1w = 0 Solving -13 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1w = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1w = 0 + 13 -1w = 0 + 13 Combine like terms: 0 + 13 = 13 -1w = 13 Divide each side by '-1'. w = -13 Simplifying w = -13

Subproblem 2

Set the factor '(12 + -1w)' equal to zero and attempt to solve: Simplifying 12 + -1w = 0 Solving 12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w = 0 + -12 -1w = 0 + -12 Combine like terms: 0 + -12 = -12 -1w = -12 Divide each side by '-1'. w = 12 Simplifying w = 12

Solution

w = {-13, 12}

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