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

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


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

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

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

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

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

Solving
-28 + -7x + 21x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-4 + -1x + 3x2) = 0

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

Ignore the factor 7.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1

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 = {-1, 1.333333333}

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