3((x-3)(8-x)-3(x-8))=x^2-28

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Solution for 3((x-3)(8-x)-3(x-8))=x^2-28 equation: 


Simplifying
3((x + -3)(8 + -1x) + -3(x + -8)) = x2 + -28

Reorder the terms:
3((-3 + x)(8 + -1x) + -3(x + -8)) = x2 + -28

Multiply (-3 + x) * (8 + -1x)
3((-3(8 + -1x) + x(8 + -1x)) + -3(x + -8)) = x2 + -28
3(((8 * -3 + -1x * -3) + x(8 + -1x)) + -3(x + -8)) = x2 + -28
3(((-24 + 3x) + x(8 + -1x)) + -3(x + -8)) = x2 + -28
3((-24 + 3x + (8 * x + -1x * x)) + -3(x + -8)) = x2 + -28
3((-24 + 3x + (8x + -1x2)) + -3(x + -8)) = x2 + -28

Combine like terms: 3x + 8x = 11x
3((-24 + 11x + -1x2) + -3(x + -8)) = x2 + -28

Reorder the terms:
3(-24 + 11x + -1x2 + -3(-8 + x)) = x2 + -28
3(-24 + 11x + -1x2 + (-8 * -3 + x * -3)) = x2 + -28
3(-24 + 11x + -1x2 + (24 + -3x)) = x2 + -28

Reorder the terms:
3(-24 + 24 + 11x + -3x + -1x2) = x2 + -28

Combine like terms: -24 + 24 = 0
3(0 + 11x + -3x + -1x2) = x2 + -28
3(11x + -3x + -1x2) = x2 + -28

Combine like terms: 11x + -3x = 8x
3(8x + -1x2) = x2 + -28
(8x * 3 + -1x2 * 3) = x2 + -28
(24x + -3x2) = x2 + -28

Reorder the terms:
24x + -3x2 = -28 + x2

Solving
24x + -3x2 = -28 + x2

Solving for variable 'x'.

Reorder the terms:
28 + 24x + -3x2 + -1x2 = -28 + x2 + 28 + -1x2

Combine like terms: -3x2 + -1x2 = -4x2
28 + 24x + -4x2 = -28 + x2 + 28 + -1x2

Reorder the terms:
28 + 24x + -4x2 = -28 + 28 + x2 + -1x2

Combine like terms: -28 + 28 = 0
28 + 24x + -4x2 = 0 + x2 + -1x2
28 + 24x + -4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
28 + 24x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + 6x + -1x2) = 0

Factor a trinomial.
4((7 + -1x)(1 + x)) = 0

Ignore the factor 4.

Subproblem 1
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

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

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {7, -1}

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