0=2x^2-3x-20

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Solution for 0=2x^2-3x-20 equation:


Simplifying
0 = 2x2 + -3x + -20

Reorder the terms:
0 = -20 + -3x + 2x2

Solving
0 = -20 + -3x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 20 = 20
20 + 3x + -2x2 = -20 + -3x + 2x2 + 20 + 3x + -2x2

Reorder the terms:
20 + 3x + -2x2 = -20 + 20 + -3x + 3x + 2x2 + -2x2

Combine like terms: -20 + 20 = 0
20 + 3x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2
20 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2

Combine like terms: -3x + 3x = 0
20 + 3x + -2x2 = 0 + 2x2 + -2x2
20 + 3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + 3x + -2x2 = 0

Factor a trinomial.
(4 + -1x)(5 + 2x) = 0

Subproblem 1

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 2

Set the factor '(5 + 2x)' equal to zero and attempt to solve: Simplifying 5 + 2x = 0 Solving 5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 2x = 0 + -5 2x = 0 + -5 Combine like terms: 0 + -5 = -5 2x = -5 Divide each side by '2'. x = -2.5 Simplifying x = -2.5

Solution

x = {4, -2.5}

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