0=-x^2+x+12

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Solution for 0=-x^2+x+12 equation:


Simplifying
0 = -1x2 + x + 12

Reorder the terms:
0 = 12 + x + -1x2

Solving
0 = 12 + x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + -12 = -12
-12 + -1x + x2 = 12 + x + -1x2 + -12 + -1x + x2

Reorder the terms:
-12 + -1x + x2 = 12 + -12 + x + -1x + -1x2 + x2

Combine like terms: 12 + -12 = 0
-12 + -1x + x2 = 0 + x + -1x + -1x2 + x2
-12 + -1x + x2 = x + -1x + -1x2 + x2

Combine like terms: x + -1x = 0
-12 + -1x + x2 = 0 + -1x2 + x2
-12 + -1x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -1x) = 0

Subproblem 1

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

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 = {-3, 4}

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