(7x-14)(5x+16)=0

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Solution for (7x-14)(5x+16)=0 equation: 


Simplifying
(7x + -14)(5x + 16) = 0

Reorder the terms:
(-14 + 7x)(5x + 16) = 0

Reorder the terms:
(-14 + 7x)(16 + 5x) = 0

Multiply (-14 + 7x) * (16 + 5x)
(-14(16 + 5x) + 7x * (16 + 5x)) = 0
((16 * -14 + 5x * -14) + 7x * (16 + 5x)) = 0
((-224 + -70x) + 7x * (16 + 5x)) = 0
(-224 + -70x + (16 * 7x + 5x * 7x)) = 0
(-224 + -70x + (112x + 35x2)) = 0

Combine like terms: -70x + 112x = 42x
(-224 + 42x + 35x2) = 0

Solving
-224 + 42x + 35x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-32 + 6x + 5x2) = 0

Factor a trinomial.
7((-16 + -5x)(2 + -1x)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-16 + -5x)' equal to zero and attempt to solve:

Simplifying
-16 + -5x = 0

Solving
-16 + -5x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -5x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5x = 0 + 16
-5x = 0 + 16

Combine like terms: 0 + 16 = 16
-5x = 16

Divide each side by '-5'.
x = -3.2

Simplifying
x = -3.2

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 = {-3.2, 2}

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