5(x-3)(4x+9)=0

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Solution for 5(x-3)(4x+9)=0 equation: 


Simplifying
5(x + -3)(4x + 9) = 0

Reorder the terms:
5(-3 + x)(4x + 9) = 0

Reorder the terms:
5(-3 + x)(9 + 4x) = 0

Multiply (-3 + x) * (9 + 4x)
5(-3(9 + 4x) + x(9 + 4x)) = 0
5((9 * -3 + 4x * -3) + x(9 + 4x)) = 0
5((-27 + -12x) + x(9 + 4x)) = 0
5(-27 + -12x + (9 * x + 4x * x)) = 0
5(-27 + -12x + (9x + 4x2)) = 0

Combine like terms: -12x + 9x = -3x
5(-27 + -3x + 4x2) = 0
(-27 * 5 + -3x * 5 + 4x2 * 5) = 0
(-135 + -15x + 20x2) = 0

Solving
-135 + -15x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-27 + -3x + 4x2) = 0

Factor a trinomial.
5((-9 + -4x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-9 + -4x)' equal to zero and attempt to solve:

Simplifying
-9 + -4x = 0

Solving
-9 + -4x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4x = 0 + 9
-4x = 0 + 9

Combine like terms: 0 + 9 = 9
-4x = 9

Divide each side by '-4'.
x = -2.25

Simplifying
x = -2.25

Subproblem 2
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
Solution
x = {-2.25, 3}

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