(5x-8)(7x+7)=0

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Solution for (5x-8)(7x+7)=0 equation: 


Simplifying
(5x + -8)(7x + 7) = 0

Reorder the terms:
(-8 + 5x)(7x + 7) = 0

Reorder the terms:
(-8 + 5x)(7 + 7x) = 0

Multiply (-8 + 5x) * (7 + 7x)
(-8(7 + 7x) + 5x * (7 + 7x)) = 0
((7 * -8 + 7x * -8) + 5x * (7 + 7x)) = 0
((-56 + -56x) + 5x * (7 + 7x)) = 0
(-56 + -56x + (7 * 5x + 7x * 5x)) = 0
(-56 + -56x + (35x + 35x2)) = 0

Combine like terms: -56x + 35x = -21x
(-56 + -21x + 35x2) = 0

Solving
-56 + -21x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-8 + -3x + 5x2) = 0

Factor a trinomial.
7((-1 + -1x)(8 + -5x)) = 0

Ignore the factor 7.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(8 + -5x)' equal to zero and attempt to solve:

Simplifying
8 + -5x = 0

Solving
8 + -5x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -5x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5x = 0 + -8
-5x = 0 + -8

Combine like terms: 0 + -8 = -8
-5x = -8

Divide each side by '-5'.
x = 1.6

Simplifying
x = 1.6
Solution
x = {-1, 1.6}

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