(x-3)(x-3)+5(x-3)+4=0

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Solution for (x-3)(x-3)+5(x-3)+4=0 equation: 


Simplifying
(x + -3)(x + -3) + 5(x + -3) + 4 = 0

Reorder the terms:
(-3 + x)(x + -3) + 5(x + -3) + 4 = 0

Reorder the terms:
(-3 + x)(-3 + x) + 5(x + -3) + 4 = 0

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) + 5(x + -3) + 4 = 0
((-3 * -3 + x * -3) + x(-3 + x)) + 5(x + -3) + 4 = 0
((9 + -3x) + x(-3 + x)) + 5(x + -3) + 4 = 0
(9 + -3x + (-3 * x + x * x)) + 5(x + -3) + 4 = 0
(9 + -3x + (-3x + x2)) + 5(x + -3) + 4 = 0

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) + 5(x + -3) + 4 = 0

Reorder the terms:
9 + -6x + x2 + 5(-3 + x) + 4 = 0
9 + -6x + x2 + (-3 * 5 + x * 5) + 4 = 0
9 + -6x + x2 + (-15 + 5x) + 4 = 0

Reorder the terms:
9 + -15 + 4 + -6x + 5x + x2 = 0

Combine like terms: 9 + -15 = -6
-6 + 4 + -6x + 5x + x2 = 0

Combine like terms: -6 + 4 = -2
-2 + -6x + 5x + x2 = 0

Combine like terms: -6x + 5x = -1x
-2 + -1x + x2 = 0

Solving
-2 + -1x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}

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