0=-28x+28x+84-3(x^2+3x)

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Solution for 0=-28x+28x+84-3(x^2+3x) equation: 


Simplifying
0 = -28x + 28x + 84 + -3(x2 + 3x)

Reorder the terms:
0 = -28x + 28x + 84 + -3(3x + x2)
0 = -28x + 28x + 84 + (3x * -3 + x2 * -3)
0 = -28x + 28x + 84 + (-9x + -3x2)

Reorder the terms:
0 = 84 + -28x + 28x + -9x + -3x2

Combine like terms: -28x + 28x = 0
0 = 84 + 0 + -9x + -3x2
0 = 84 + -9x + -3x2

Solving
0 = 84 + -9x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + -84 = -84
-84 + 9x + 3x2 = 84 + -9x + -3x2 + -84 + 9x + 3x2

Reorder the terms:
-84 + 9x + 3x2 = 84 + -84 + -9x + 9x + -3x2 + 3x2

Combine like terms: 84 + -84 = 0
-84 + 9x + 3x2 = 0 + -9x + 9x + -3x2 + 3x2
-84 + 9x + 3x2 = -9x + 9x + -3x2 + 3x2

Combine like terms: -9x + 9x = 0
-84 + 9x + 3x2 = 0 + -3x2 + 3x2
-84 + 9x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-84 + 9x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + 3x + x2) = 0

Factor a trinomial.
3((-7 + -1x)(4 + -1x)) = 0

Ignore the factor 3.

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 '(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 = {-7, 4}

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