3x(x-1)-x^2-20=0

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Solution for 3x(x-1)-x^2-20=0 equation:


Simplifying
3x(x + -1) + -1x2 + -20 = 0

Reorder the terms:
3x(-1 + x) + -1x2 + -20 = 0
(-1 * 3x + x * 3x) + -1x2 + -20 = 0
(-3x + 3x2) + -1x2 + -20 = 0

Reorder the terms:
-20 + -3x + 3x2 + -1x2 = 0

Combine like terms: 3x2 + -1x2 = 2x2
-20 + -3x + 2x2 = 0

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

Solving for variable 'x'.

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

Subproblem 1

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

Subproblem 2

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

Solution

x = {-2.5, 4}

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