-7(4x-16)(-2x-9)=0

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Solution for -7(4x-16)(-2x-9)=0 equation: 


Simplifying
-7(4x + -16)(-2x + -9) = 0

Reorder the terms:
-7(-16 + 4x)(-2x + -9) = 0

Reorder the terms:
-7(-16 + 4x)(-9 + -2x) = 0

Multiply (-16 + 4x) * (-9 + -2x)
-7(-16(-9 + -2x) + 4x * (-9 + -2x)) = 0
-7((-9 * -16 + -2x * -16) + 4x * (-9 + -2x)) = 0
-7((144 + 32x) + 4x * (-9 + -2x)) = 0
-7(144 + 32x + (-9 * 4x + -2x * 4x)) = 0
-7(144 + 32x + (-36x + -8x2)) = 0

Combine like terms: 32x + -36x = -4x
-7(144 + -4x + -8x2) = 0
(144 * -7 + -4x * -7 + -8x2 * -7) = 0
(-1008 + 28x + 56x2) = 0

Solving
-1008 + 28x + 56x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '28'.
28(-36 + x + 2x2) = 0

Factor a trinomial.
28((-9 + -2x)(4 + -1x)) = 0

Ignore the factor 28.

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

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 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 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

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 = {-4.5, 4}

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