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

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


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

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

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

Multiply (-7 + 4x) * (5 + 7x)
2(-7(5 + 7x) + 4x * (5 + 7x)) = 0
2((5 * -7 + 7x * -7) + 4x * (5 + 7x)) = 0
2((-35 + -49x) + 4x * (5 + 7x)) = 0
2(-35 + -49x + (5 * 4x + 7x * 4x)) = 0
2(-35 + -49x + (20x + 28x2)) = 0

Combine like terms: -49x + 20x = -29x
2(-35 + -29x + 28x2) = 0
(-35 * 2 + -29x * 2 + 28x2 * 2) = 0
(-70 + -58x + 56x2) = 0

Solving
-70 + -58x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + -29x + 28x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

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

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

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Solution
x = {-0.7142857143, 1.75}

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