4x(5x-3)=84

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Solution for 4x(5x-3)=84 equation:


Simplifying
4x(5x + -3) = 84

Reorder the terms:
4x(-3 + 5x) = 84
(-3 * 4x + 5x * 4x) = 84
(-12x + 20x2) = 84

Solving
-12x + 20x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + -12x + 20x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -12x + 20x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-21 + -3x + 5x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-21 + -3x + 5x2)' equal to zero and attempt to solve: Simplifying -21 + -3x + 5x2 = 0 Solving -21 + -3x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + -0.6x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -0.6x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -0.6x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -0.6x + x2 = 0 + 4.2 -0.6x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -0.6x + x2 = 4.2 The x term is -0.6x. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6x + 0.09 + x2 = 4.2 + 0.09 Reorder the terms: 0.09 + -0.6x + x2 = 4.2 + 0.09 Combine like terms: 4.2 + 0.09 = 4.29 0.09 + -0.6x + x2 = 4.29 Factor a perfect square on the left side: (x + -0.3)(x + -0.3) = 4.29 Calculate the square root of the right side: 2.071231518 Break this problem into two subproblems by setting (x + -0.3) equal to 2.071231518 and -2.071231518.

Subproblem 1

x + -0.3 = 2.071231518 Simplifying x + -0.3 = 2.071231518 Reorder the terms: -0.3 + x = 2.071231518 Solving -0.3 + x = 2.071231518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 2.071231518 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.071231518 + 0.3 x = 2.071231518 + 0.3 Combine like terms: 2.071231518 + 0.3 = 2.371231518 x = 2.371231518 Simplifying x = 2.371231518

Subproblem 2

x + -0.3 = -2.071231518 Simplifying x + -0.3 = -2.071231518 Reorder the terms: -0.3 + x = -2.071231518 Solving -0.3 + x = -2.071231518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -2.071231518 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.071231518 + 0.3 x = -2.071231518 + 0.3 Combine like terms: -2.071231518 + 0.3 = -1.771231518 x = -1.771231518 Simplifying x = -1.771231518

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.371231518, -1.771231518}

Solution

x = {2.371231518, -1.771231518}

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