Question

Please solve by factorization:
x² - 30x + 216 = 0

Answer 1

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Simplifying

x2 + 30x + -216 = 0

Reorder the terms:

-216 + 30x + x2 = 0

Solving

-216 + 30x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-36 + -1x)(6 + -1x) = 0

Subproblem 1

Set the factor '(-36 + -1x)' equal to zero and attempt to solve:

Simplifying

-36 + -1x = 0

Solving

-36 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '36' to each side of the equation.

-36 + 36 + -1x = 0 + 36

Combine like terms: -36 + 36 = 0

0 + -1x = 0 + 36

-1x = 0 + 36

Combine like terms: 0 + 36 = 36

-1x = 36

Divide each side by '-1'.

x = -36

Simplifying

x = -36

Subproblem 2

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

Solution

x = {-36, 6}

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Answer 2

Factorisation:-

${x}^{2} - 30x + 216 \\ = {x}^{2} - 18x - 12x + 216 \\ = x(x - 18) - 12(x - 18) \\ = (x - 18)(x - 12)$
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