(5x-7)(6x+4)=0

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Solution for (5x-7)(6x+4)=0 equation: 


Simplifying
(5x + -7)(6x + 4) = 0

Reorder the terms:
(-7 + 5x)(6x + 4) = 0

Reorder the terms:
(-7 + 5x)(4 + 6x) = 0

Multiply (-7 + 5x) * (4 + 6x)
(-7(4 + 6x) + 5x * (4 + 6x)) = 0
((4 * -7 + 6x * -7) + 5x * (4 + 6x)) = 0
((-28 + -42x) + 5x * (4 + 6x)) = 0
(-28 + -42x + (4 * 5x + 6x * 5x)) = 0
(-28 + -42x + (20x + 30x2)) = 0

Combine like terms: -42x + 20x = -22x
(-28 + -22x + 30x2) = 0

Solving
-28 + -22x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + -11x + 15x2) = 0

Factor a trinomial.
2((-2 + -3x)(7 + -5x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4
Solution
x = {-0.6666666667, 1.4}

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