(3x-7)(8x+2)=0

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Solution for (3x-7)(8x+2)=0 equation: 


Simplifying
(3x + -7)(8x + 2) = 0

Reorder the terms:
(-7 + 3x)(8x + 2) = 0

Reorder the terms:
(-7 + 3x)(2 + 8x) = 0

Multiply (-7 + 3x) * (2 + 8x)
(-7(2 + 8x) + 3x * (2 + 8x)) = 0
((2 * -7 + 8x * -7) + 3x * (2 + 8x)) = 0
((-14 + -56x) + 3x * (2 + 8x)) = 0
(-14 + -56x + (2 * 3x + 8x * 3x)) = 0
(-14 + -56x + (6x + 24x2)) = 0

Combine like terms: -56x + 6x = -50x
(-14 + -50x + 24x2) = 0

Solving
-14 + -50x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -25x + 12x2) = 0

Factor a trinomial.
2((-1 + -4x)(7 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1 + -4x)' equal to zero and attempt to solve:

Simplifying
-1 + -4x = 0

Solving
-1 + -4x = 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 + -4x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4x = 0 + 1
-4x = 0 + 1

Combine like terms: 0 + 1 = 1
-4x = 1

Divide each side by '-4'.
x = -0.25

Simplifying
x = -0.25

Subproblem 2
Set the factor '(7 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {-0.25, 2.333333333}

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