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

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


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

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

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

Multiply (-4 + 3x) * (4 + 7x)
(-4(4 + 7x) + 3x * (4 + 7x)) = 0
((4 * -4 + 7x * -4) + 3x * (4 + 7x)) = 0
((-16 + -28x) + 3x * (4 + 7x)) = 0
(-16 + -28x + (4 * 3x + 7x * 3x)) = 0
(-16 + -28x + (12x + 21x2)) = 0

Combine like terms: -28x + 12x = -16x
(-16 + -16x + 21x2) = 0

Solving
-16 + -16x + 21x2 = 0

Solving for variable 'x'.

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


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

Simplifying
-4 + -7x = 0

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

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

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

Divide each side by '-7'.
x = -0.5714285714

Simplifying
x = -0.5714285714

Subproblem 2
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
Solution
x = {-0.5714285714, 1.333333333}

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