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

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


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

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

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

Combine like terms: 14x + -32x = -18x
(56 + -18x + -8x2) = 0

Solving
56 + -18x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(28 + -9x + -4x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {1.75, -4}

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