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

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


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

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

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

Multiply (-8 + 4x) * (2 + 7x)
(-8(2 + 7x) + 4x * (2 + 7x)) = 0
((2 * -8 + 7x * -8) + 4x * (2 + 7x)) = 0
((-16 + -56x) + 4x * (2 + 7x)) = 0
(-16 + -56x + (2 * 4x + 7x * 4x)) = 0
(-16 + -56x + (8x + 28x2)) = 0

Combine like terms: -56x + 8x = -48x
(-16 + -48x + 28x2) = 0

Solving
-16 + -48x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + -12x + 7x2) = 0

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

Ignore the factor 4.

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 '(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
Solution
x = {-0.2857142857, 2}

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