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

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


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

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

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

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

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

Solving
-28 + -16x + 12x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 4.

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 '(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, 2.333333333}

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