(x-3)(x+3)=7x-21

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Solution for (x-3)(x+3)=7x-21 equation: 


Simplifying
(x + -3)(x + 3) = 7x + -21

Reorder the terms:
(-3 + x)(x + 3) = 7x + -21

Reorder the terms:
(-3 + x)(3 + x) = 7x + -21

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) = 7x + -21
((3 * -3 + x * -3) + x(3 + x)) = 7x + -21
((-9 + -3x) + x(3 + x)) = 7x + -21
(-9 + -3x + (3 * x + x * x)) = 7x + -21
(-9 + -3x + (3x + x2)) = 7x + -21

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) = 7x + -21
(-9 + x2) = 7x + -21

Reorder the terms:
-9 + x2 = -21 + 7x

Solving
-9 + x2 = -21 + 7x

Solving for variable 'x'.

Reorder the terms:
-9 + 21 + -7x + x2 = -21 + 7x + 21 + -7x

Combine like terms: -9 + 21 = 12
12 + -7x + x2 = -21 + 7x + 21 + -7x

Reorder the terms:
12 + -7x + x2 = -21 + 21 + 7x + -7x

Combine like terms: -21 + 21 = 0
12 + -7x + x2 = 0 + 7x + -7x
12 + -7x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
12 + -7x + x2 = 0

Factor a trinomial.
(3 + -1x)(4 + -1x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {3, 4}

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