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

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


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

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

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

Multiply (-9 + x) * (7 + 3x)
4(-9(7 + 3x) + x(7 + 3x)) = 0
4((7 * -9 + 3x * -9) + x(7 + 3x)) = 0
4((-63 + -27x) + x(7 + 3x)) = 0
4(-63 + -27x + (7 * x + 3x * x)) = 0
4(-63 + -27x + (7x + 3x2)) = 0

Combine like terms: -27x + 7x = -20x
4(-63 + -20x + 3x2) = 0
(-63 * 4 + -20x * 4 + 3x2 * 4) = 0
(-252 + -80x + 12x2) = 0

Solving
-252 + -80x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-63 + -20x + 3x2) = 0

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

Ignore the factor 4.

Subproblem 1
Set the factor '(-7 + -3x)' equal to zero and attempt to solve:

Simplifying
-7 + -3x = 0

Solving
-7 + -3x = 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 + -3x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3x = 0 + 7
-3x = 0 + 7

Combine like terms: 0 + 7 = 7
-3x = 7

Divide each side by '-3'.
x = -2.333333333

Simplifying
x = -2.333333333

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 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 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2.333333333, 9}

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