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

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


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

Reorder the terms:
(-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((-4 + -1x)(7 + -4x)) = 0

Ignore the factor 2.

Subproblem 1
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

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 = {-4, 1.75}

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