4x(x-9)-4(x-7)(X+7)=16

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Solution for 4x(x-9)-4(x-7)(X+7)=16 equation:


Simplifying
4x(x + -9) + -4(x + -7)(X + 7) = 16

Reorder the terms:
4x(-9 + x) + -4(x + -7)(X + 7) = 16
(-9 * 4x + x * 4x) + -4(x + -7)(X + 7) = 16
(-36x + 4x2) + -4(x + -7)(X + 7) = 16

Reorder the terms:
-36x + 4x2 + -4(-7 + x)(X + 7) = 16

Reorder the terms:
-36x + 4x2 + -4(-7 + x)(7 + X) = 16

Multiply (-7 + x) * (7 + X)
-36x + 4x2 + -4(-7(7 + X) + x(7 + X)) = 16
-36x + 4x2 + -4((7 * -7 + X * -7) + x(7 + X)) = 16
-36x + 4x2 + -4((-49 + -7X) + x(7 + X)) = 16
-36x + 4x2 + -4(-49 + -7X + (7 * x + X * x)) = 16
-36x + 4x2 + -4(-49 + -7X + (7x + xX)) = 16
-36x + 4x2 + -4(-49 + -7X + 7x + xX) = 16
-36x + 4x2 + (-49 * -4 + -7X * -4 + 7x * -4 + xX * -4) = 16
-36x + 4x2 + (196 + 28X + -28x + -4xX) = 16

Reorder the terms:
196 + 28X + -36x + -28x + -4xX + 4x2 = 16

Combine like terms: -36x + -28x = -64x
196 + 28X + -64x + -4xX + 4x2 = 16

Solving
196 + 28X + -64x + -4xX + 4x2 = 16

Solving for variable 'X'.

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

Add '-196' to each side of the equation.
196 + 28X + -64x + -4xX + -196 + 4x2 = 16 + -196

Reorder the terms:
196 + -196 + 28X + -64x + -4xX + 4x2 = 16 + -196

Combine like terms: 196 + -196 = 0
0 + 28X + -64x + -4xX + 4x2 = 16 + -196
28X + -64x + -4xX + 4x2 = 16 + -196

Combine like terms: 16 + -196 = -180
28X + -64x + -4xX + 4x2 = -180

Add '64x' to each side of the equation.
28X + -64x + -4xX + 64x + 4x2 = -180 + 64x

Reorder the terms:
28X + -64x + 64x + -4xX + 4x2 = -180 + 64x

Combine like terms: -64x + 64x = 0
28X + 0 + -4xX + 4x2 = -180 + 64x
28X + -4xX + 4x2 = -180 + 64x

Add '-4x2' to each side of the equation.
28X + -4xX + 4x2 + -4x2 = -180 + 64x + -4x2

Combine like terms: 4x2 + -4x2 = 0
28X + -4xX + 0 = -180 + 64x + -4x2
28X + -4xX = -180 + 64x + -4x2

Reorder the terms:
180 + 28X + -64x + -4xX + 4x2 = -180 + 64x + -4x2 + 180 + -64x + 4x2

Reorder the terms:
180 + 28X + -64x + -4xX + 4x2 = -180 + 180 + 64x + -64x + -4x2 + 4x2

Combine like terms: -180 + 180 = 0
180 + 28X + -64x + -4xX + 4x2 = 0 + 64x + -64x + -4x2 + 4x2
180 + 28X + -64x + -4xX + 4x2 = 64x + -64x + -4x2 + 4x2

Combine like terms: 64x + -64x = 0
180 + 28X + -64x + -4xX + 4x2 = 0 + -4x2 + 4x2
180 + 28X + -64x + -4xX + 4x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
180 + 28X + -64x + -4xX + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(45 + 7X + -16x + -1xX + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(45 + 7X + -16x + -1xX + x2)' equal to zero and attempt to solve: Simplifying 45 + 7X + -16x + -1xX + x2 = 0 Solving 45 + 7X + -16x + -1xX + x2 = 0 Move all terms containing X to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + 7X + -16x + -1xX + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 7X + -16x + -1xX + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 7X + -16x + -1xX + x2 = 0 + -45 7X + -16x + -1xX + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 7X + -16x + -1xX + x2 = -45 Add '16x' to each side of the equation. 7X + -16x + -1xX + 16x + x2 = -45 + 16x Reorder the terms: 7X + -16x + 16x + -1xX + x2 = -45 + 16x Combine like terms: -16x + 16x = 0 7X + 0 + -1xX + x2 = -45 + 16x 7X + -1xX + x2 = -45 + 16x Add '-1x2' to each side of the equation. 7X + -1xX + x2 + -1x2 = -45 + 16x + -1x2 Combine like terms: x2 + -1x2 = 0 7X + -1xX + 0 = -45 + 16x + -1x2 7X + -1xX = -45 + 16x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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