(x-2)(x-3)=(x+3)2

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Solution for (x-2)(x-3)=(x+3)2 equation:


Simplifying
(x + -2)(x + -3) = (x + 3) * 2

Reorder the terms:
(-2 + x)(x + -3) = (x + 3) * 2

Reorder the terms:
(-2 + x)(-3 + x) = (x + 3) * 2

Multiply (-2 + x) * (-3 + x)
(-2(-3 + x) + x(-3 + x)) = (x + 3) * 2
((-3 * -2 + x * -2) + x(-3 + x)) = (x + 3) * 2
((6 + -2x) + x(-3 + x)) = (x + 3) * 2
(6 + -2x + (-3 * x + x * x)) = (x + 3) * 2
(6 + -2x + (-3x + x2)) = (x + 3) * 2

Combine like terms: -2x + -3x = -5x
(6 + -5x + x2) = (x + 3) * 2

Reorder the terms:
6 + -5x + x2 = (3 + x) * 2

Reorder the terms for easier multiplication:
6 + -5x + x2 = 2(3 + x)
6 + -5x + x2 = (3 * 2 + x * 2)
6 + -5x + x2 = (6 + 2x)

Add '-6' to each side of the equation.
6 + -5x + -6 + x2 = 6 + -6 + 2x

Reorder the terms:
6 + -6 + -5x + x2 = 6 + -6 + 2x

Combine like terms: 6 + -6 = 0
0 + -5x + x2 = 6 + -6 + 2x
-5x + x2 = 6 + -6 + 2x

Combine like terms: 6 + -6 = 0
-5x + x2 = 0 + 2x
-5x + x2 = 2x

Solving
-5x + x2 = 2x

Solving for variable 'x'.

Reorder the terms:
-5x + -2x + x2 = 2x + -2x

Combine like terms: -5x + -2x = -7x
-7x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-7x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-7 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Simplifying
x = 7
Solution
x = {0, 7}

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