3(x-7)(3x+4)=0

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Solution for 3(x-7)(3x+4)=0 equation: 


Simplifying
3(x + -7)(3x + 4) = 0

Reorder the terms:
3(-7 + x)(3x + 4) = 0

Reorder the terms:
3(-7 + x)(4 + 3x) = 0

Multiply (-7 + x) * (4 + 3x)
3(-7(4 + 3x) + x(4 + 3x)) = 0
3((4 * -7 + 3x * -7) + x(4 + 3x)) = 0
3((-28 + -21x) + x(4 + 3x)) = 0
3(-28 + -21x + (4 * x + 3x * x)) = 0
3(-28 + -21x + (4x + 3x2)) = 0

Combine like terms: -21x + 4x = -17x
3(-28 + -17x + 3x2) = 0
(-28 * 3 + -17x * 3 + 3x2 * 3) = 0
(-84 + -51x + 9x2) = 0

Solving
-84 + -51x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -17x + 3x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 7}

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