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

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


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

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

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

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

Combine like terms: -16x + 28x = 12x
(-56 + 12x + 8x2) = 0

Solving
-56 + 12x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + 3x + 2x2) = 0

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

Ignore the factor 4.

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

Simplifying
-7 + -2x = 0

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

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

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

Divide each side by '-2'.
x = -3.5

Simplifying
x = -3.5

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 = {-3.5, 2}

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