8(x-4)=7x(x+4)

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Solution for 8(x-4)=7x(x+4) equation:


Simplifying
8(x + -4) = 7x(x + 4)

Reorder the terms:
8(-4 + x) = 7x(x + 4)
(-4 * 8 + x * 8) = 7x(x + 4)
(-32 + 8x) = 7x(x + 4)

Reorder the terms:
-32 + 8x = 7x(4 + x)
-32 + 8x = (4 * 7x + x * 7x)
-32 + 8x = (28x + 7x2)

Solving
-32 + 8x = 28x + 7x2

Solving for variable 'x'.

Combine like terms: 8x + -28x = -20x
-32 + -20x + -7x2 = 28x + 7x2 + -28x + -7x2

Reorder the terms:
-32 + -20x + -7x2 = 28x + -28x + 7x2 + -7x2

Combine like terms: 28x + -28x = 0
-32 + -20x + -7x2 = 0 + 7x2 + -7x2
-32 + -20x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
-32 + -20x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(32 + 20x + 7x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(32 + 20x + 7x2)' equal to zero and attempt to solve: Simplifying 32 + 20x + 7x2 = 0 Solving 32 + 20x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 4.571428571 + 2.857142857x + x2 = 0 Move the constant term to the right: Add '-4.571428571' to each side of the equation. 4.571428571 + 2.857142857x + -4.571428571 + x2 = 0 + -4.571428571 Reorder the terms: 4.571428571 + -4.571428571 + 2.857142857x + x2 = 0 + -4.571428571 Combine like terms: 4.571428571 + -4.571428571 = 0.000000000 0.000000000 + 2.857142857x + x2 = 0 + -4.571428571 2.857142857x + x2 = 0 + -4.571428571 Combine like terms: 0 + -4.571428571 = -4.571428571 2.857142857x + x2 = -4.571428571 The x term is 2.857142857x. Take half its coefficient (1.428571429). Square it (2.040816328) and add it to both sides. Add '2.040816328' to each side of the equation. 2.857142857x + 2.040816328 + x2 = -4.571428571 + 2.040816328 Reorder the terms: 2.040816328 + 2.857142857x + x2 = -4.571428571 + 2.040816328 Combine like terms: -4.571428571 + 2.040816328 = -2.530612243 2.040816328 + 2.857142857x + x2 = -2.530612243 Factor a perfect square on the left side: (x + 1.428571429)(x + 1.428571429) = -2.530612243 Can't calculate square root of the right side. 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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