(6x-4)(3x+7)=0

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Solution for (6x-4)(3x+7)=0 equation: 


Simplifying
(6x + -4)(3x + 7) = 0

Reorder the terms:
(-4 + 6x)(3x + 7) = 0

Reorder the terms:
(-4 + 6x)(7 + 3x) = 0

Multiply (-4 + 6x) * (7 + 3x)
(-4(7 + 3x) + 6x * (7 + 3x)) = 0
((7 * -4 + 3x * -4) + 6x * (7 + 3x)) = 0
((-28 + -12x) + 6x * (7 + 3x)) = 0
(-28 + -12x + (7 * 6x + 3x * 6x)) = 0
(-28 + -12x + (42x + 18x2)) = 0

Combine like terms: -12x + 42x = 30x
(-28 + 30x + 18x2) = 0

Solving
-28 + 30x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 15x + 9x2) = 0

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

Ignore the factor 2.

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 '(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 = {-2.333333333, 0.6666666667}

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