(g+17)(g-2)=20

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Solution for (g+17)(g-2)=20 equation:


Simplifying
(g + 17)(g + -2) = 20

Reorder the terms:
(17 + g)(g + -2) = 20

Reorder the terms:
(17 + g)(-2 + g) = 20

Multiply (17 + g) * (-2 + g)
(17(-2 + g) + g(-2 + g)) = 20
((-2 * 17 + g * 17) + g(-2 + g)) = 20
((-34 + 17g) + g(-2 + g)) = 20
(-34 + 17g + (-2 * g + g * g)) = 20
(-34 + 17g + (-2g + g2)) = 20

Combine like terms: 17g + -2g = 15g
(-34 + 15g + g2) = 20

Solving
-34 + 15g + g2 = 20

Solving for variable 'g'.

Reorder the terms:
-34 + -20 + 15g + g2 = 20 + -20

Combine like terms: -34 + -20 = -54
-54 + 15g + g2 = 20 + -20

Combine like terms: 20 + -20 = 0
-54 + 15g + g2 = 0

Factor a trinomial.
(-18 + -1g)(3 + -1g) = 0

Subproblem 1

Set the factor '(-18 + -1g)' equal to zero and attempt to solve: Simplifying -18 + -1g = 0 Solving -18 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + -1g = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -1g = 0 + 18 -1g = 0 + 18 Combine like terms: 0 + 18 = 18 -1g = 18 Divide each side by '-1'. g = -18 Simplifying g = -18

Subproblem 2

Set the factor '(3 + -1g)' equal to zero and attempt to solve: Simplifying 3 + -1g = 0 Solving 3 + -1g = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1g = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1g = 0 + -3 -1g = 0 + -3 Combine like terms: 0 + -3 = -3 -1g = -3 Divide each side by '-1'. g = 3 Simplifying g = 3

Solution

g = {-18, 3}

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