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

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


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

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

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

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

Combine like terms: -28x + 18x = -10x
(-12 + -10x + 42x2) = 0

Solving
-12 + -10x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + -5x + 21x2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + -7x)' equal to zero and attempt to solve:

Simplifying
-3 + -7x = 0

Solving
-3 + -7x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -7x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7x = 0 + 3
-7x = 0 + 3

Combine like terms: 0 + 3 = 3
-7x = 3

Divide each side by '-7'.
x = -0.4285714286

Simplifying
x = -0.4285714286

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 = {-0.4285714286, 0.6666666667}

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