(x-3)(x+3)=5x-13

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Solution for (x-3)(x+3)=5x-13 equation: 


Simplifying
(x + -3)(x + 3) = 5x + -13

Reorder the terms:
(-3 + x)(x + 3) = 5x + -13

Reorder the terms:
(-3 + x)(3 + x) = 5x + -13

Multiply (-3 + x) * (3 + x)
(-3(3 + x) + x(3 + x)) = 5x + -13
((3 * -3 + x * -3) + x(3 + x)) = 5x + -13
((-9 + -3x) + x(3 + x)) = 5x + -13
(-9 + -3x + (3 * x + x * x)) = 5x + -13
(-9 + -3x + (3x + x2)) = 5x + -13

Combine like terms: -3x + 3x = 0
(-9 + 0 + x2) = 5x + -13
(-9 + x2) = 5x + -13

Reorder the terms:
-9 + x2 = -13 + 5x

Solving
-9 + x2 = -13 + 5x

Solving for variable 'x'.

Reorder the terms:
-9 + 13 + -5x + x2 = -13 + 5x + 13 + -5x

Combine like terms: -9 + 13 = 4
4 + -5x + x2 = -13 + 5x + 13 + -5x

Reorder the terms:
4 + -5x + x2 = -13 + 13 + 5x + -5x

Combine like terms: -13 + 13 = 0
4 + -5x + x2 = 0 + 5x + -5x
4 + -5x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
4 + -5x + x2 = 0

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


Subproblem 1
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

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 = {1, 4}

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