2(w+1)=-6(w+1)(w-2)+7(w-2)

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Solution for 2(w+1)=-6(w+1)(w-2)+7(w-2) equation:


Simplifying
2(w + 1) = -6(w + 1)(w + -2) + 7(w + -2)

Reorder the terms:
2(1 + w) = -6(w + 1)(w + -2) + 7(w + -2)
(1 * 2 + w * 2) = -6(w + 1)(w + -2) + 7(w + -2)
(2 + 2w) = -6(w + 1)(w + -2) + 7(w + -2)

Reorder the terms:
2 + 2w = -6(1 + w)(w + -2) + 7(w + -2)

Reorder the terms:
2 + 2w = -6(1 + w)(-2 + w) + 7(w + -2)

Multiply (1 + w) * (-2 + w)
2 + 2w = -6(1(-2 + w) + w(-2 + w)) + 7(w + -2)
2 + 2w = -6((-2 * 1 + w * 1) + w(-2 + w)) + 7(w + -2)
2 + 2w = -6((-2 + 1w) + w(-2 + w)) + 7(w + -2)
2 + 2w = -6(-2 + 1w + (-2 * w + w * w)) + 7(w + -2)
2 + 2w = -6(-2 + 1w + (-2w + w2)) + 7(w + -2)

Combine like terms: 1w + -2w = -1w
2 + 2w = -6(-2 + -1w + w2) + 7(w + -2)
2 + 2w = (-2 * -6 + -1w * -6 + w2 * -6) + 7(w + -2)
2 + 2w = (12 + 6w + -6w2) + 7(w + -2)

Reorder the terms:
2 + 2w = 12 + 6w + -6w2 + 7(-2 + w)
2 + 2w = 12 + 6w + -6w2 + (-2 * 7 + w * 7)
2 + 2w = 12 + 6w + -6w2 + (-14 + 7w)

Reorder the terms:
2 + 2w = 12 + -14 + 6w + 7w + -6w2

Combine like terms: 12 + -14 = -2
2 + 2w = -2 + 6w + 7w + -6w2

Combine like terms: 6w + 7w = 13w
2 + 2w = -2 + 13w + -6w2

Solving
2 + 2w = -2 + 13w + -6w2

Solving for variable 'w'.

Reorder the terms:
2 + 2 + 2w + -13w + 6w2 = -2 + 13w + -6w2 + 2 + -13w + 6w2

Combine like terms: 2 + 2 = 4
4 + 2w + -13w + 6w2 = -2 + 13w + -6w2 + 2 + -13w + 6w2

Combine like terms: 2w + -13w = -11w
4 + -11w + 6w2 = -2 + 13w + -6w2 + 2 + -13w + 6w2

Reorder the terms:
4 + -11w + 6w2 = -2 + 2 + 13w + -13w + -6w2 + 6w2

Combine like terms: -2 + 2 = 0
4 + -11w + 6w2 = 0 + 13w + -13w + -6w2 + 6w2
4 + -11w + 6w2 = 13w + -13w + -6w2 + 6w2

Combine like terms: 13w + -13w = 0
4 + -11w + 6w2 = 0 + -6w2 + 6w2
4 + -11w + 6w2 = -6w2 + 6w2

Combine like terms: -6w2 + 6w2 = 0
4 + -11w + 6w2 = 0

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


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

Simplifying
1 + -2w = 0

Solving
1 + -2w = 0

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

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

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

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

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5

Subproblem 2
Set the factor '(4 + -3w)' equal to zero and attempt to solve:

Simplifying
4 + -3w = 0

Solving
4 + -3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3w = 0 + -4
-3w = 0 + -4

Combine like terms: 0 + -4 = -4
-3w = -4

Divide each side by '-3'.
w = 1.333333333

Simplifying
w = 1.333333333
Solution
w = {0.5, 1.333333333}

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