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

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


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

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

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

Multiply (-4 + 7x) * (2 + 7x)
5(-4(2 + 7x) + 7x * (2 + 7x)) = 0
5((2 * -4 + 7x * -4) + 7x * (2 + 7x)) = 0
5((-8 + -28x) + 7x * (2 + 7x)) = 0
5(-8 + -28x + (2 * 7x + 7x * 7x)) = 0
5(-8 + -28x + (14x + 49x2)) = 0

Combine like terms: -28x + 14x = -14x
5(-8 + -14x + 49x2) = 0
(-8 * 5 + -14x * 5 + 49x2 * 5) = 0
(-40 + -70x + 245x2) = 0

Solving
-40 + -70x + 245x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + -14x + 49x2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + -7x)' equal to zero and attempt to solve:

Simplifying
-2 + -7x = 0

Solving
-2 + -7x = 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 + -7x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7x = 0 + 2
-7x = 0 + 2

Combine like terms: 0 + 2 = 2
-7x = 2

Divide each side by '-7'.
x = -0.2857142857

Simplifying
x = -0.2857142857

Subproblem 2
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
Solution
x = {-0.2857142857, 0.5714285714}

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