3(4x-7)(2+2x)=0

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Solution for 3(4x-7)(2+2x)=0 equation: 


Simplifying
3(4x + -7)(2 + 2x) = 0

Reorder the terms:
3(-7 + 4x)(2 + 2x) = 0

Multiply (-7 + 4x) * (2 + 2x)
3(-7(2 + 2x) + 4x * (2 + 2x)) = 0
3((2 * -7 + 2x * -7) + 4x * (2 + 2x)) = 0
3((-14 + -14x) + 4x * (2 + 2x)) = 0
3(-14 + -14x + (2 * 4x + 2x * 4x)) = 0
3(-14 + -14x + (8x + 8x2)) = 0

Combine like terms: -14x + 8x = -6x
3(-14 + -6x + 8x2) = 0
(-14 * 3 + -6x * 3 + 8x2 * 3) = 0
(-42 + -18x + 24x2) = 0

Solving
-42 + -18x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -3x + 4x2) = 0

Factor a trinomial.
6((-1 + -1x)(7 + -4x)) = 0

Ignore the factor 6.

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 + -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
Solution
x = {-1, 1.75}

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