3(x-5)=2x(x+5)

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Solution for 3(x-5)=2x(x+5) equation:


Simplifying
3(x + -5) = 2x(x + 5)

Reorder the terms:
3(-5 + x) = 2x(x + 5)
(-5 * 3 + x * 3) = 2x(x + 5)
(-15 + 3x) = 2x(x + 5)

Reorder the terms:
-15 + 3x = 2x(5 + x)
-15 + 3x = (5 * 2x + x * 2x)
-15 + 3x = (10x + 2x2)

Solving
-15 + 3x = 10x + 2x2

Solving for variable 'x'.

Combine like terms: 3x + -10x = -7x
-15 + -7x + -2x2 = 10x + 2x2 + -10x + -2x2

Reorder the terms:
-15 + -7x + -2x2 = 10x + -10x + 2x2 + -2x2

Combine like terms: 10x + -10x = 0
-15 + -7x + -2x2 = 0 + 2x2 + -2x2
-15 + -7x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + -7x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(15 + 7x + 2x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(15 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 15 + 7x + 2x2 = 0 Solving 15 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 3.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 3.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 3.5x + x2 = 0 + -7.5 3.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 3.5x + x2 = -7.5 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -7.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -7.5 + 3.0625 Combine like terms: -7.5 + 3.0625 = -4.4375 3.0625 + 3.5x + x2 = -4.4375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -4.4375 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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