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

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


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

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

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

Multiply (-4 + x) * (7 + 4x)
3(-4(7 + 4x) + x(7 + 4x)) = 0
3((7 * -4 + 4x * -4) + x(7 + 4x)) = 0
3((-28 + -16x) + x(7 + 4x)) = 0
3(-28 + -16x + (7 * x + 4x * x)) = 0
3(-28 + -16x + (7x + 4x2)) = 0

Combine like terms: -16x + 7x = -9x
3(-28 + -9x + 4x2) = 0
(-28 * 3 + -9x * 3 + 4x2 * 3) = 0
(-84 + -27x + 12x2) = 0

Solving
-84 + -27x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-28 + -9x + 4x2) = 0

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

Ignore the factor 3.

Subproblem 1
Set the factor '(-7 + -4x)' equal to zero and attempt to solve:

Simplifying
-7 + -4x = 0

Solving
-7 + -4x = 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 + -4x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -4x = 0 + 7
-4x = 0 + 7

Combine like terms: 0 + 7 = 7
-4x = 7

Divide each side by '-4'.
x = -1.75

Simplifying
x = -1.75

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 = {-1.75, 4}

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