(3+11x)-(2x+5)(3+2x)=0

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Solution for (3+11x)-(2x+5)(3+2x)=0 equation:


Simplifying
(3 + 11x) + -1(2x + 5)(3 + 2x) = 0

Remove parenthesis around (3 + 11x)
3 + 11x + -1(2x + 5)(3 + 2x) = 0

Reorder the terms:
3 + 11x + -1(5 + 2x)(3 + 2x) = 0

Multiply (5 + 2x) * (3 + 2x)
3 + 11x + -1(5(3 + 2x) + 2x * (3 + 2x)) = 0
3 + 11x + -1((3 * 5 + 2x * 5) + 2x * (3 + 2x)) = 0
3 + 11x + -1((15 + 10x) + 2x * (3 + 2x)) = 0
3 + 11x + -1(15 + 10x + (3 * 2x + 2x * 2x)) = 0
3 + 11x + -1(15 + 10x + (6x + 4x2)) = 0

Combine like terms: 10x + 6x = 16x
3 + 11x + -1(15 + 16x + 4x2) = 0
3 + 11x + (15 * -1 + 16x * -1 + 4x2 * -1) = 0
3 + 11x + (-15 + -16x + -4x2) = 0

Reorder the terms:
3 + -15 + 11x + -16x + -4x2 = 0

Combine like terms: 3 + -15 = -12
-12 + 11x + -16x + -4x2 = 0

Combine like terms: 11x + -16x = -5x
-12 + -5x + -4x2 = 0

Solving
-12 + -5x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 5x + 4x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(12 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying 12 + 5x + 4x2 = 0 Solving 12 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3 + 1.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 1.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 1.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 1.25x + x2 = 0 + -3 1.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 1.25x + x2 = -3 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -3 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -3 + 0.390625 Combine like terms: -3 + 0.390625 = -2.609375 0.390625 + 1.25x + x2 = -2.609375 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = -2.609375 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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