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

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Solution for 4(x-7)(x-5)=0 equation: 


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

Reorder the terms:
4(-7 + x)(x + -5) = 0

Reorder the terms:
4(-7 + x)(-5 + x) = 0

Multiply (-7 + x) * (-5 + x)
4(-7(-5 + x) + x(-5 + x)) = 0
4((-5 * -7 + x * -7) + x(-5 + x)) = 0
4((35 + -7x) + x(-5 + x)) = 0
4(35 + -7x + (-5 * x + x * x)) = 0
4(35 + -7x + (-5x + x2)) = 0

Combine like terms: -7x + -5x = -12x
4(35 + -12x + x2) = 0
(35 * 4 + -12x * 4 + x2 * 4) = 0
(140 + -48x + 4x2) = 0

Solving
140 + -48x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(35 + -12x + x2) = 0

Factor a trinomial.
4((5 + -1x)(7 + -1x)) = 0

Ignore the factor 4.

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 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 = {5, 7}

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