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

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


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

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

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

Multiply (-7 + 5x) * (-2 + x)
3(-7(-2 + x) + 5x * (-2 + x)) = 0
3((-2 * -7 + x * -7) + 5x * (-2 + x)) = 0
3((14 + -7x) + 5x * (-2 + x)) = 0
3(14 + -7x + (-2 * 5x + x * 5x)) = 0
3(14 + -7x + (-10x + 5x2)) = 0

Combine like terms: -7x + -10x = -17x
3(14 + -17x + 5x2) = 0
(14 * 3 + -17x * 3 + 5x2 * 3) = 0
(42 + -51x + 15x2) = 0

Solving
42 + -51x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -17x + 5x2) = 0

Factor a trinomial.
3((7 + -5x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + -5x)' equal to zero and attempt to solve:

Simplifying
7 + -5x = 0

Solving
7 + -5x = 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 + -5x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5x = 0 + -7
-5x = 0 + -7

Combine like terms: 0 + -7 = -7
-5x = -7

Divide each side by '-5'.
x = 1.4

Simplifying
x = 1.4

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 = {1.4, 2}

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