2x^2=x^2-x+12

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


Simplifying
2x2 = x2 + -1x + 12

Reorder the terms:
2x2 = 12 + -1x + x2

Solving
2x2 = 12 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-12 + x + 2x2 + -1x2 = 12 + -1x + x2 + -12 + x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-12 + x + 1x2 = 12 + -1x + x2 + -12 + x + -1x2

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

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

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

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

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

Solution

x = {-4, 3}

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