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

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


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

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

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

Multiply (-2 + 3x) * (7 + 4x)
2(-2(7 + 4x) + 3x * (7 + 4x)) = 0
2((7 * -2 + 4x * -2) + 3x * (7 + 4x)) = 0
2((-14 + -8x) + 3x * (7 + 4x)) = 0
2(-14 + -8x + (7 * 3x + 4x * 3x)) = 0
2(-14 + -8x + (21x + 12x2)) = 0

Combine like terms: -8x + 21x = 13x
2(-14 + 13x + 12x2) = 0
(-14 * 2 + 13x * 2 + 12x2 * 2) = 0
(-28 + 26x + 24x2) = 0

Solving
-28 + 26x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 13x + 12x2) = 0

Factor a trinomial.
2((-7 + -4x)(2 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-1.75, 0.6666666667}

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