x^2-12x+39=3x-5

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Solution for x^2-12x+39=3x-5 equation:


Simplifying
x2 + -12x + 39 = 3x + -5

Reorder the terms:
39 + -12x + x2 = 3x + -5

Reorder the terms:
39 + -12x + x2 = -5 + 3x

Solving
39 + -12x + x2 = -5 + 3x

Solving for variable 'x'.

Reorder the terms:
39 + 5 + -12x + -3x + x2 = -5 + 3x + 5 + -3x

Combine like terms: 39 + 5 = 44
44 + -12x + -3x + x2 = -5 + 3x + 5 + -3x

Combine like terms: -12x + -3x = -15x
44 + -15x + x2 = -5 + 3x + 5 + -3x

Reorder the terms:
44 + -15x + x2 = -5 + 5 + 3x + -3x

Combine like terms: -5 + 5 = 0
44 + -15x + x2 = 0 + 3x + -3x
44 + -15x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
44 + -15x + x2 = 0

Factor a trinomial.
(4 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11

Solution

x = {4, 11}

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