-3(-x+7)5x=-21

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Solution for -3(-x+7)5x=-21 equation:


Simplifying
-3(-1x + 7) * 5x = -21

Reorder the terms:
-3(7 + -1x) * 5x = -21

Reorder the terms for easier multiplication:
-3 * 5x(7 + -1x) = -21

Multiply -3 * 5
-15x(7 + -1x) = -21
(7 * -15x + -1x * -15x) = -21
(-105x + 15x2) = -21

Solving
-105x + 15x2 = -21

Solving for variable 'x'.

Reorder the terms:
21 + -105x + 15x2 = -21 + 21

Combine like terms: -21 + 21 = 0
21 + -105x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + -35x + 5x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(7 + -35x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + -35x + 5x2 = 0 Solving 7 + -35x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -7x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -7x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -7x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -7x + x2 = 0 + -1.4 -7x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -7x + x2 = -1.4 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1.4 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.4 + 12.25 Combine like terms: -1.4 + 12.25 = 10.85 12.25 + -7x + x2 = 10.85 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 10.85 Calculate the square root of the right side: 3.293933818 Break this problem into two subproblems by setting (x + -3.5) equal to 3.293933818 and -3.293933818.

Subproblem 1

x + -3.5 = 3.293933818 Simplifying x + -3.5 = 3.293933818 Reorder the terms: -3.5 + x = 3.293933818 Solving -3.5 + x = 3.293933818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.293933818 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.293933818 + 3.5 x = 3.293933818 + 3.5 Combine like terms: 3.293933818 + 3.5 = 6.793933818 x = 6.793933818 Simplifying x = 6.793933818

Subproblem 2

x + -3.5 = -3.293933818 Simplifying x + -3.5 = -3.293933818 Reorder the terms: -3.5 + x = -3.293933818 Solving -3.5 + x = -3.293933818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.293933818 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.293933818 + 3.5 x = -3.293933818 + 3.5 Combine like terms: -3.293933818 + 3.5 = 0.206066182 x = 0.206066182 Simplifying x = 0.206066182

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.793933818, 0.206066182}

Solution

x = {6.793933818, 0.206066182}

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