5(x+3)(x-4)=0

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Solution for 5(x+3)(x-4)=0 equation: 


Simplifying
5(x + 3)(x + -4) = 0

Reorder the terms:
5(3 + x)(x + -4) = 0

Reorder the terms:
5(3 + x)(-4 + x) = 0

Multiply (3 + x) * (-4 + x)
5(3(-4 + x) + x(-4 + x)) = 0
5((-4 * 3 + x * 3) + x(-4 + x)) = 0
5((-12 + 3x) + x(-4 + x)) = 0
5(-12 + 3x + (-4 * x + x * x)) = 0
5(-12 + 3x + (-4x + x2)) = 0

Combine like terms: 3x + -4x = -1x
5(-12 + -1x + x2) = 0
(-12 * 5 + -1x * 5 + x2 * 5) = 0
(-60 + -5x + 5x2) = 0

Solving
-60 + -5x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-12 + -1x + x2) = 0

Factor a trinomial.
5((-3 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}

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