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

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


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

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

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

Multiply (-7 + 3x) * (7 + 4x)
(-7(7 + 4x) + 3x * (7 + 4x)) = 0
((7 * -7 + 4x * -7) + 3x * (7 + 4x)) = 0
((-49 + -28x) + 3x * (7 + 4x)) = 0
(-49 + -28x + (7 * 3x + 4x * 3x)) = 0
(-49 + -28x + (21x + 12x2)) = 0

Combine like terms: -28x + 21x = -7x
(-49 + -7x + 12x2) = 0

Solving
-49 + -7x + 12x2 = 0

Solving for variable 'x'.

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


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 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-1.75, 2.333333333}

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