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

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


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

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

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

Multiply (-4 + 7x) * (8 + 4x)
(-4(8 + 4x) + 7x * (8 + 4x)) = 0
((8 * -4 + 4x * -4) + 7x * (8 + 4x)) = 0
((-32 + -16x) + 7x * (8 + 4x)) = 0
(-32 + -16x + (8 * 7x + 4x * 7x)) = 0
(-32 + -16x + (56x + 28x2)) = 0

Combine like terms: -16x + 56x = 40x
(-32 + 40x + 28x2) = 0

Solving
-32 + 40x + 28x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + 10x + 7x2) = 0

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

Ignore the factor 4.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-2, 0.5714285714}

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