(x-3)(x-3)=4(11-x)

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Solution for (x-3)(x-3)=4(11-x) equation: 


Simplifying
(x + -3)(x + -3) = 4(11 + -1x)

Reorder the terms:
(-3 + x)(x + -3) = 4(11 + -1x)

Reorder the terms:
(-3 + x)(-3 + x) = 4(11 + -1x)

Multiply (-3 + x) * (-3 + x)
(-3(-3 + x) + x(-3 + x)) = 4(11 + -1x)
((-3 * -3 + x * -3) + x(-3 + x)) = 4(11 + -1x)
((9 + -3x) + x(-3 + x)) = 4(11 + -1x)
(9 + -3x + (-3 * x + x * x)) = 4(11 + -1x)
(9 + -3x + (-3x + x2)) = 4(11 + -1x)

Combine like terms: -3x + -3x = -6x
(9 + -6x + x2) = 4(11 + -1x)
9 + -6x + x2 = (11 * 4 + -1x * 4)
9 + -6x + x2 = (44 + -4x)

Solving
9 + -6x + x2 = 44 + -4x

Solving for variable 'x'.

Reorder the terms:
9 + -44 + -6x + 4x + x2 = 44 + -4x + -44 + 4x

Combine like terms: 9 + -44 = -35
-35 + -6x + 4x + x2 = 44 + -4x + -44 + 4x

Combine like terms: -6x + 4x = -2x
-35 + -2x + x2 = 44 + -4x + -44 + 4x

Reorder the terms:
-35 + -2x + x2 = 44 + -44 + -4x + 4x

Combine like terms: 44 + -44 = 0
-35 + -2x + x2 = 0 + -4x + 4x
-35 + -2x + x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-35 + -2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}

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