12x+21=3(4x+6)5(x+8)-7

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Solution for 12x+21=3(4x+6)5(x+8)-7 equation:


Simplifying
12x + 21 = 3(4x + 6) * 5(x + 8) + -7

Reorder the terms:
21 + 12x = 3(4x + 6) * 5(x + 8) + -7

Reorder the terms:
21 + 12x = 3(6 + 4x) * 5(x + 8) + -7

Reorder the terms:
21 + 12x = 3(6 + 4x) * 5(8 + x) + -7

Reorder the terms for easier multiplication:
21 + 12x = 3 * 5(6 + 4x)(8 + x) + -7

Multiply 3 * 5
21 + 12x = 15(6 + 4x)(8 + x) + -7

Multiply (6 + 4x) * (8 + x)
21 + 12x = 15(6(8 + x) + 4x * (8 + x)) + -7
21 + 12x = 15((8 * 6 + x * 6) + 4x * (8 + x)) + -7
21 + 12x = 15((48 + 6x) + 4x * (8 + x)) + -7
21 + 12x = 15(48 + 6x + (8 * 4x + x * 4x)) + -7
21 + 12x = 15(48 + 6x + (32x + 4x2)) + -7

Combine like terms: 6x + 32x = 38x
21 + 12x = 15(48 + 38x + 4x2) + -7
21 + 12x = (48 * 15 + 38x * 15 + 4x2 * 15) + -7
21 + 12x = (720 + 570x + 60x2) + -7

Reorder the terms:
21 + 12x = 720 + -7 + 570x + 60x2

Combine like terms: 720 + -7 = 713
21 + 12x = 713 + 570x + 60x2

Solving
21 + 12x = 713 + 570x + 60x2

Solving for variable 'x'.

Reorder the terms:
21 + -713 + 12x + -570x + -60x2 = 713 + 570x + 60x2 + -713 + -570x + -60x2

Combine like terms: 21 + -713 = -692
-692 + 12x + -570x + -60x2 = 713 + 570x + 60x2 + -713 + -570x + -60x2

Combine like terms: 12x + -570x = -558x
-692 + -558x + -60x2 = 713 + 570x + 60x2 + -713 + -570x + -60x2

Reorder the terms:
-692 + -558x + -60x2 = 713 + -713 + 570x + -570x + 60x2 + -60x2

Combine like terms: 713 + -713 = 0
-692 + -558x + -60x2 = 0 + 570x + -570x + 60x2 + -60x2
-692 + -558x + -60x2 = 570x + -570x + 60x2 + -60x2

Combine like terms: 570x + -570x = 0
-692 + -558x + -60x2 = 0 + 60x2 + -60x2
-692 + -558x + -60x2 = 60x2 + -60x2

Combine like terms: 60x2 + -60x2 = 0
-692 + -558x + -60x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(346 + 279x + 30x2) = 0

Ignore the factor -2.

Subproblem 1

Set the factor '(346 + 279x + 30x2)' equal to zero and attempt to solve: Simplifying 346 + 279x + 30x2 = 0 Solving 346 + 279x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 11.53333333 + 9.3x + x2 = 0.0 Move the constant term to the right: Add '-11.53333333' to each side of the equation. 11.53333333 + 9.3x + -11.53333333 + x2 = 0.0 + -11.53333333 Reorder the terms: 11.53333333 + -11.53333333 + 9.3x + x2 = 0.0 + -11.53333333 Combine like terms: 11.53333333 + -11.53333333 = 0.00000000 0.00000000 + 9.3x + x2 = 0.0 + -11.53333333 9.3x + x2 = 0.0 + -11.53333333 Combine like terms: 0.0 + -11.53333333 = -11.53333333 9.3x + x2 = -11.53333333 The x term is 9.3x. Take half its coefficient (4.65). Square it (21.6225) and add it to both sides. Add '21.6225' to each side of the equation. 9.3x + 21.6225 + x2 = -11.53333333 + 21.6225 Reorder the terms: 21.6225 + 9.3x + x2 = -11.53333333 + 21.6225 Combine like terms: -11.53333333 + 21.6225 = 10.08916667 21.6225 + 9.3x + x2 = 10.08916667 Factor a perfect square on the left side: (x + 4.65)(x + 4.65) = 10.08916667 Calculate the square root of the right side: 3.17634486 Break this problem into two subproblems by setting (x + 4.65) equal to 3.17634486 and -3.17634486.

Subproblem 1

x + 4.65 = 3.17634486 Simplifying x + 4.65 = 3.17634486 Reorder the terms: 4.65 + x = 3.17634486 Solving 4.65 + x = 3.17634486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.65' to each side of the equation. 4.65 + -4.65 + x = 3.17634486 + -4.65 Combine like terms: 4.65 + -4.65 = 0.00 0.00 + x = 3.17634486 + -4.65 x = 3.17634486 + -4.65 Combine like terms: 3.17634486 + -4.65 = -1.47365514 x = -1.47365514 Simplifying x = -1.47365514

Subproblem 2

x + 4.65 = -3.17634486 Simplifying x + 4.65 = -3.17634486 Reorder the terms: 4.65 + x = -3.17634486 Solving 4.65 + x = -3.17634486 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.65' to each side of the equation. 4.65 + -4.65 + x = -3.17634486 + -4.65 Combine like terms: 4.65 + -4.65 = 0.00 0.00 + x = -3.17634486 + -4.65 x = -3.17634486 + -4.65 Combine like terms: -3.17634486 + -4.65 = -7.82634486 x = -7.82634486 Simplifying x = -7.82634486

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.47365514, -7.82634486}

Solution

x = {-1.47365514, -7.82634486}

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