0=-x^2-x+30

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Solution for 0=-x^2-x+30 equation:


Simplifying
0 = -1x2 + -1x + 30

Reorder the terms:
0 = 30 + -1x + -1x2

Solving
0 = 30 + -1x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -30 = -30
-30 + x + x2 = 30 + -1x + -1x2 + -30 + x + x2

Reorder the terms:
-30 + x + x2 = 30 + -30 + -1x + x + -1x2 + x2

Combine like terms: 30 + -30 = 0
-30 + x + x2 = 0 + -1x + x + -1x2 + x2
-30 + x + x2 = -1x + x + -1x2 + x2

Combine like terms: -1x + x = 0
-30 + x + x2 = 0 + -1x2 + x2
-30 + x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-30 + x + x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -1x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-6, 5}

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