2(7x-3)(5-x)=0

Solution for 2(7x-3)(5-x)=0 equation:

Simplifying
2(7x + -3)(5 + -1x) = 0

Reorder the terms:
2(-3 + 7x)(5 + -1x) = 0

Multiply (-3 + 7x) * (5 + -1x)
2(-3(5 + -1x) + 7x * (5 + -1x)) = 0
2((5 * -3 + -1x * -3) + 7x * (5 + -1x)) = 0
2((-15 + 3x) + 7x * (5 + -1x)) = 0
2(-15 + 3x + (5 * 7x + -1x * 7x)) = 0
2(-15 + 3x + (35x + -7x2)) = 0

Combine like terms: 3x + 35x = 38x
2(-15 + 38x + -7x2) = 0
(-15 * 2 + 38x * 2 + -7x2 * 2) = 0
(-30 + 76x + -14x2) = 0

Solving
-30 + 76x + -14x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 38x + -7x2) = 0

Factor a trinomial.
2((-5 + x)(3 + -7x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

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

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

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

Simplifying
x = 5
Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -7x = 0 + -3

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

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

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {5, 0.4285714286}