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

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


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

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

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

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

Combine like terms: -28x + 8x = -20x
(-56 + -20x + 4x2) = 0

Solving
-56 + -20x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-14 + -5x + x2) = 0

Factor a trinomial.
4((-2 + -1x)(7 + -1x)) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2, 7}

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