3(4x-7)(2x-7)=0

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Solution for 3(4x-7)(2x-7)=0 equation: 


Simplifying
3(4x + -7)(2x + -7) = 0

Reorder the terms:
3(-7 + 4x)(2x + -7) = 0

Reorder the terms:
3(-7 + 4x)(-7 + 2x) = 0

Multiply (-7 + 4x) * (-7 + 2x)
3(-7(-7 + 2x) + 4x * (-7 + 2x)) = 0
3((-7 * -7 + 2x * -7) + 4x * (-7 + 2x)) = 0
3((49 + -14x) + 4x * (-7 + 2x)) = 0
3(49 + -14x + (-7 * 4x + 2x * 4x)) = 0
3(49 + -14x + (-28x + 8x2)) = 0

Combine like terms: -14x + -28x = -42x
3(49 + -42x + 8x2) = 0
(49 * 3 + -42x * 3 + 8x2 * 3) = 0
(147 + -126x + 24x2) = 0

Solving
147 + -126x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(49 + -42x + 8x2) = 0

Factor a trinomial.
3((7 + -4x)(7 + -2x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75

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

Simplifying
7 + -2x = 0

Solving
7 + -2x = 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 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {1.75, 3.5}

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