(2x-8)(7x+4)=0

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Solution for (2x-8)(7x+4)=0 equation: 


Simplifying
(2x + -8)(7x + 4) = 0

Reorder the terms:
(-8 + 2x)(7x + 4) = 0

Reorder the terms:
(-8 + 2x)(4 + 7x) = 0

Multiply (-8 + 2x) * (4 + 7x)
(-8(4 + 7x) + 2x * (4 + 7x)) = 0
((4 * -8 + 7x * -8) + 2x * (4 + 7x)) = 0
((-32 + -56x) + 2x * (4 + 7x)) = 0
(-32 + -56x + (4 * 2x + 7x * 2x)) = 0
(-32 + -56x + (8x + 14x2)) = 0

Combine like terms: -56x + 8x = -48x
(-32 + -48x + 14x2) = 0

Solving
-32 + -48x + 14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + -24x + 7x2) = 0

Factor a trinomial.
2((-4 + -7x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-0.5714285714, 4}

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