x^2=-12x+45

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Solution for x^2=-12x+45 equation:


Simplifying
x2 = -12x + 45

Reorder the terms:
x2 = 45 + -12x

Solving
x2 = 45 + -12x

Solving for variable 'x'.

Reorder the terms:
-45 + 12x + x2 = 45 + -12x + -45 + 12x

Reorder the terms:
-45 + 12x + x2 = 45 + -45 + -12x + 12x

Combine like terms: 45 + -45 = 0
-45 + 12x + x2 = 0 + -12x + 12x
-45 + 12x + x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
-45 + 12x + x2 = 0

Factor a trinomial.
(-15 + -1x)(3 + -1x) = 0

Subproblem 1

Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15

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 = {-15, 3}

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