-4x(x-3)=6(x+5)

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Solution for -4x(x-3)=6(x+5) equation:


Simplifying
-4x(x + -3) = 6(x + 5)

Reorder the terms:
-4x(-3 + x) = 6(x + 5)
(-3 * -4x + x * -4x) = 6(x + 5)
(12x + -4x2) = 6(x + 5)

Reorder the terms:
12x + -4x2 = 6(5 + x)
12x + -4x2 = (5 * 6 + x * 6)
12x + -4x2 = (30 + 6x)

Solving
12x + -4x2 = 30 + 6x

Solving for variable 'x'.

Reorder the terms:
-30 + 12x + -6x + -4x2 = 30 + 6x + -30 + -6x

Combine like terms: 12x + -6x = 6x
-30 + 6x + -4x2 = 30 + 6x + -30 + -6x

Reorder the terms:
-30 + 6x + -4x2 = 30 + -30 + 6x + -6x

Combine like terms: 30 + -30 = 0
-30 + 6x + -4x2 = 0 + 6x + -6x
-30 + 6x + -4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-30 + 6x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 3x + -2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-15 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying -15 + 3x + -2x2 = 0 Solving -15 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -1.5x + -7.5 + x2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -1.5x + x2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -1.5x + x2 = 0 + -7.5 -1.5x + x2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -1.5x + x2 = -7.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -7.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -7.5 + 0.5625 Combine like terms: -7.5 + 0.5625 = -6.9375 0.5625 + -1.5x + x2 = -6.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -6.9375 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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