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

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


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

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

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

Multiply (-7 + x) * (3 + x)
5(-7(3 + x) + x(3 + x)) = 0
5((3 * -7 + x * -7) + x(3 + x)) = 0
5((-21 + -7x) + x(3 + x)) = 0
5(-21 + -7x + (3 * x + x * x)) = 0
5(-21 + -7x + (3x + x2)) = 0

Combine like terms: -7x + 3x = -4x
5(-21 + -4x + x2) = 0
(-21 * 5 + -4x * 5 + x2 * 5) = 0
(-105 + -20x + 5x2) = 0

Solving
-105 + -20x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -4x + x2) = 0

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

Ignore the factor 5.

Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 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 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 7}

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