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

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


Simplifying
6(7 + -4x) * x + -8(-3x + 5) = 0

Reorder the terms for easier multiplication:
6x(7 + -4x) + -8(-3x + 5) = 0
(7 * 6x + -4x * 6x) + -8(-3x + 5) = 0
(42x + -24x2) + -8(-3x + 5) = 0

Reorder the terms:
42x + -24x2 + -8(5 + -3x) = 0
42x + -24x2 + (5 * -8 + -3x * -8) = 0
42x + -24x2 + (-40 + 24x) = 0

Reorder the terms:
-40 + 42x + 24x + -24x2 = 0

Combine like terms: 42x + 24x = 66x
-40 + 66x + -24x2 = 0

Solving
-40 + 66x + -24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 33x + -12x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-20 + 33x + -12x2)' equal to zero and attempt to solve: Simplifying -20 + 33x + -12x2 = 0 Solving -20 + 33x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 1.666666667 + -2.75x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -2.75x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -2.75x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -2.75x + x2 = 0 + -1.666666667 -2.75x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -2.75x + x2 = -1.666666667 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = -1.666666667 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = -1.666666667 + 1.890625 Combine like terms: -1.666666667 + 1.890625 = 0.223958333 1.890625 + -2.75x + x2 = 0.223958333 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 0.223958333 Calculate the square root of the right side: 0.473242362 Break this problem into two subproblems by setting (x + -1.375) equal to 0.473242362 and -0.473242362.

Subproblem 1

x + -1.375 = 0.473242362 Simplifying x + -1.375 = 0.473242362 Reorder the terms: -1.375 + x = 0.473242362 Solving -1.375 + x = 0.473242362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 0.473242362 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 0.473242362 + 1.375 x = 0.473242362 + 1.375 Combine like terms: 0.473242362 + 1.375 = 1.848242362 x = 1.848242362 Simplifying x = 1.848242362

Subproblem 2

x + -1.375 = -0.473242362 Simplifying x + -1.375 = -0.473242362 Reorder the terms: -1.375 + x = -0.473242362 Solving -1.375 + x = -0.473242362 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -0.473242362 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -0.473242362 + 1.375 x = -0.473242362 + 1.375 Combine like terms: -0.473242362 + 1.375 = 0.901757638 x = 0.901757638 Simplifying x = 0.901757638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.848242362, 0.901757638}

Solution

x = {1.848242362, 0.901757638}

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