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

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


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

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

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

Multiply (4 + 2x) * (-5 + 7x)
(4(-5 + 7x) + 2x * (-5 + 7x)) = 0
((-5 * 4 + 7x * 4) + 2x * (-5 + 7x)) = 0
((-20 + 28x) + 2x * (-5 + 7x)) = 0
(-20 + 28x + (-5 * 2x + 7x * 2x)) = 0
(-20 + 28x + (-10x + 14x2)) = 0

Combine like terms: 28x + -10x = 18x
(-20 + 18x + 14x2) = 0

Solving
-20 + 18x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 9x + 7x2) = 0

Factor a trinomial.
2((-2 + -1x)(5 + -7x)) = 0

Ignore the factor 2.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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

Simplifying
5 + -7x = 0

Solving
5 + -7x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -7x = 0 + -5

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

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

Divide each side by '-7'.
x = 0.7142857143

Simplifying
x = 0.7142857143
Solution
x = {-2, 0.7142857143}

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