x+24=(x-6)(x-6)

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Solution for x+24=(x-6)(x-6) equation: 


Simplifying
x + 24 = (x + -6)(x + -6)

Reorder the terms:
24 + x = (x + -6)(x + -6)

Reorder the terms:
24 + x = (-6 + x)(x + -6)

Reorder the terms:
24 + x = (-6 + x)(-6 + x)

Multiply (-6 + x) * (-6 + x)
24 + x = (-6(-6 + x) + x(-6 + x))
24 + x = ((-6 * -6 + x * -6) + x(-6 + x))
24 + x = ((36 + -6x) + x(-6 + x))
24 + x = (36 + -6x + (-6 * x + x * x))
24 + x = (36 + -6x + (-6x + x2))

Combine like terms: -6x + -6x = -12x
24 + x = (36 + -12x + x2)

Solving
24 + x = 36 + -12x + x2

Solving for variable 'x'.

Reorder the terms:
24 + -36 + x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2

Combine like terms: 24 + -36 = -12
-12 + x + 12x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2

Combine like terms: x + 12x = 13x
-12 + 13x + -1x2 = 36 + -12x + x2 + -36 + 12x + -1x2

Reorder the terms:
-12 + 13x + -1x2 = 36 + -36 + -12x + 12x + x2 + -1x2

Combine like terms: 36 + -36 = 0
-12 + 13x + -1x2 = 0 + -12x + 12x + x2 + -1x2
-12 + 13x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
-12 + 13x + -1x2 = 0 + x2 + -1x2
-12 + 13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 13x + -1x2 = 0

Factor a trinomial.
(-12 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve:

Simplifying
-12 + x = 0

Solving
-12 + x = 0

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

Add '12' to each side of the equation.
-12 + 12 + x = 0 + 12

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

Combine like terms: 0 + 12 = 12
x = 12

Simplifying
x = 12

Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {12, 1}

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