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

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


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

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

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

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

Combine like terms: 12x + -14x = -2x
(-8 + -2x + 21x2) = 0

Solving
-8 + -2x + 21x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-4 + -7x)' equal to zero and attempt to solve:

Simplifying
-4 + -7x = 0

Solving
-4 + -7x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -7x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -7x = 0 + 4
-7x = 0 + 4

Combine like terms: 0 + 4 = 4
-7x = 4

Divide each side by '-7'.
x = -0.5714285714

Simplifying
x = -0.5714285714

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 = {-0.5714285714, 0.6666666667}

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