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

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


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

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

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

Multiply (-7 + x) * (-5 + 2x)
5(-7(-5 + 2x) + x(-5 + 2x)) = 0
5((-5 * -7 + 2x * -7) + x(-5 + 2x)) = 0
5((35 + -14x) + x(-5 + 2x)) = 0
5(35 + -14x + (-5 * x + 2x * x)) = 0
5(35 + -14x + (-5x + 2x2)) = 0

Combine like terms: -14x + -5x = -19x
5(35 + -19x + 2x2) = 0
(35 * 5 + -19x * 5 + 2x2 * 5) = 0
(175 + -95x + 10x2) = 0

Solving
175 + -95x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(35 + -19x + 2x2) = 0

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

Ignore the factor 5.

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2.5, 7}

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