3(x-7)(4x+9)=0

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Solution for 3(x-7)(4x+9)=0 equation: 


Simplifying
3(x + -7)(4x + 9) = 0

Reorder the terms:
3(-7 + x)(4x + 9) = 0

Reorder the terms:
3(-7 + x)(9 + 4x) = 0

Multiply (-7 + x) * (9 + 4x)
3(-7(9 + 4x) + x(9 + 4x)) = 0
3((9 * -7 + 4x * -7) + x(9 + 4x)) = 0
3((-63 + -28x) + x(9 + 4x)) = 0
3(-63 + -28x + (9 * x + 4x * x)) = 0
3(-63 + -28x + (9x + 4x2)) = 0

Combine like terms: -28x + 9x = -19x
3(-63 + -19x + 4x2) = 0
(-63 * 3 + -19x * 3 + 4x2 * 3) = 0
(-189 + -57x + 12x2) = 0

Solving
-189 + -57x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-63 + -19x + 4x2) = 0

Factor a trinomial.
3((-9 + -4x)(7 + -1x)) = 0

Ignore the factor 3.

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 '(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 = {-2.25, 7}

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