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

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


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

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

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

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

Combine like terms: -12x + 49x = 37x
(-28 + 37x + 21x2) = 0

Solving
-28 + 37x + 21x2 = 0

Solving for variable 'x'.

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {-2.333333333, 0.5714285714}

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