560=8w(w+3)

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Solution for 560=8w(w+3) equation:


Simplifying
560 = 8w(w + 3)

Reorder the terms:
560 = 8w(3 + w)
560 = (3 * 8w + w * 8w)
560 = (24w + 8w2)

Solving
560 = 24w + 8w2

Solving for variable 'w'.

Reorder the terms:
560 + -24w + -8w2 = 24w + -24w + 8w2 + -8w2

Combine like terms: 24w + -24w = 0
560 + -24w + -8w2 = 0 + 8w2 + -8w2
560 + -24w + -8w2 = 8w2 + -8w2

Combine like terms: 8w2 + -8w2 = 0
560 + -24w + -8w2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(70 + -3w + -1w2) = 0

Factor a trinomial.
8((7 + -1w)(10 + w)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7

Subproblem 2

Set the factor '(10 + w)' equal to zero and attempt to solve: Simplifying 10 + w = 0 Solving 10 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + w = 0 + -10 Combine like terms: 10 + -10 = 0 0 + w = 0 + -10 w = 0 + -10 Combine like terms: 0 + -10 = -10 w = -10 Simplifying w = -10

Solution

w = {7, -10}

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