(2x+1)(3x-2)=5(4x-1)

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Solution for (2x+1)(3x-2)=5(4x-1) equation:


Simplifying
(2x + 1)(3x + -2) = 5(4x + -1)

Reorder the terms:
(1 + 2x)(3x + -2) = 5(4x + -1)

Reorder the terms:
(1 + 2x)(-2 + 3x) = 5(4x + -1)

Multiply (1 + 2x) * (-2 + 3x)
(1(-2 + 3x) + 2x * (-2 + 3x)) = 5(4x + -1)
((-2 * 1 + 3x * 1) + 2x * (-2 + 3x)) = 5(4x + -1)
((-2 + 3x) + 2x * (-2 + 3x)) = 5(4x + -1)
(-2 + 3x + (-2 * 2x + 3x * 2x)) = 5(4x + -1)
(-2 + 3x + (-4x + 6x2)) = 5(4x + -1)

Combine like terms: 3x + -4x = -1x
(-2 + -1x + 6x2) = 5(4x + -1)

Reorder the terms:
-2 + -1x + 6x2 = 5(-1 + 4x)
-2 + -1x + 6x2 = (-1 * 5 + 4x * 5)
-2 + -1x + 6x2 = (-5 + 20x)

Solving
-2 + -1x + 6x2 = -5 + 20x

Solving for variable 'x'.

Reorder the terms:
-2 + 5 + -1x + -20x + 6x2 = -5 + 20x + 5 + -20x

Combine like terms: -2 + 5 = 3
3 + -1x + -20x + 6x2 = -5 + 20x + 5 + -20x

Combine like terms: -1x + -20x = -21x
3 + -21x + 6x2 = -5 + 20x + 5 + -20x

Reorder the terms:
3 + -21x + 6x2 = -5 + 5 + 20x + -20x

Combine like terms: -5 + 5 = 0
3 + -21x + 6x2 = 0 + 20x + -20x
3 + -21x + 6x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
3 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -7x + 2x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + -7x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + -7x + 2x2 = 0 Solving 1 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.5x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.5x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.5x + x2 = 0 + -0.5 -3.5x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.5x + x2 = -0.5 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 = -0.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -0.5 + 3.0625 Combine like terms: -0.5 + 3.0625 = 2.5625 3.0625 + -3.5x + x2 = 2.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 2.5625 Calculate the square root of the right side: 1.600781059 Break this problem into two subproblems by setting (x + -1.75) equal to 1.600781059 and -1.600781059.

Subproblem 1

x + -1.75 = 1.600781059 Simplifying x + -1.75 = 1.600781059 Reorder the terms: -1.75 + x = 1.600781059 Solving -1.75 + x = 1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.600781059 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.600781059 + 1.75 x = 1.600781059 + 1.75 Combine like terms: 1.600781059 + 1.75 = 3.350781059 x = 3.350781059 Simplifying x = 3.350781059

Subproblem 2

x + -1.75 = -1.600781059 Simplifying x + -1.75 = -1.600781059 Reorder the terms: -1.75 + x = -1.600781059 Solving -1.75 + x = -1.600781059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.600781059 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.600781059 + 1.75 x = -1.600781059 + 1.75 Combine like terms: -1.600781059 + 1.75 = 0.149218941 x = 0.149218941 Simplifying x = 0.149218941

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.350781059, 0.149218941}

Solution

x = {3.350781059, 0.149218941}

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