2(6-4x)(5x+7)=0

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Solution for 2(6-4x)(5x+7)=0 equation: 


Simplifying
2(6 + -4x)(5x + 7) = 0

Reorder the terms:
2(6 + -4x)(7 + 5x) = 0

Multiply (6 + -4x) * (7 + 5x)
2(6(7 + 5x) + -4x * (7 + 5x)) = 0
2((7 * 6 + 5x * 6) + -4x * (7 + 5x)) = 0
2((42 + 30x) + -4x * (7 + 5x)) = 0
2(42 + 30x + (7 * -4x + 5x * -4x)) = 0
2(42 + 30x + (-28x + -20x2)) = 0

Combine like terms: 30x + -28x = 2x
2(42 + 2x + -20x2) = 0
(42 * 2 + 2x * 2 + -20x2 * 2) = 0
(84 + 4x + -40x2) = 0

Solving
84 + 4x + -40x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + x + -10x2) = 0

Factor a trinomial.
4((3 + -2x)(7 + 5x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, -1.4}

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