7(z-3)6z-4=

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Solution for 7(z-3)6z-4= equation:


Simplifying
7(z + -3) * 6z + -4 = 0

Reorder the terms:
7(-3 + z) * 6z + -4 = 0

Reorder the terms for easier multiplication:
7 * 6z(-3 + z) + -4 = 0

Multiply 7 * 6
42z(-3 + z) + -4 = 0
(-3 * 42z + z * 42z) + -4 = 0
(-126z + 42z2) + -4 = 0

Reorder the terms:
-4 + -126z + 42z2 = 0

Solving
-4 + -126z + 42z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -63z + 21z2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-2 + -63z + 21z2)' equal to zero and attempt to solve: Simplifying -2 + -63z + 21z2 = 0 Solving -2 + -63z + 21z2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.09523809524 + -3z + z2 = 0 Move the constant term to the right: Add '0.09523809524' to each side of the equation. -0.09523809524 + -3z + 0.09523809524 + z2 = 0 + 0.09523809524 Reorder the terms: -0.09523809524 + 0.09523809524 + -3z + z2 = 0 + 0.09523809524 Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000 0.00000000000 + -3z + z2 = 0 + 0.09523809524 -3z + z2 = 0 + 0.09523809524 Combine like terms: 0 + 0.09523809524 = 0.09523809524 -3z + z2 = 0.09523809524 The z term is -3z. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3z + 2.25 + z2 = 0.09523809524 + 2.25 Reorder the terms: 2.25 + -3z + z2 = 0.09523809524 + 2.25 Combine like terms: 0.09523809524 + 2.25 = 2.34523809524 2.25 + -3z + z2 = 2.34523809524 Factor a perfect square on the left side: (z + -1.5)(z + -1.5) = 2.34523809524 Calculate the square root of the right side: 1.531417022 Break this problem into two subproblems by setting (z + -1.5) equal to 1.531417022 and -1.531417022.

Subproblem 1

z + -1.5 = 1.531417022 Simplifying z + -1.5 = 1.531417022 Reorder the terms: -1.5 + z = 1.531417022 Solving -1.5 + z = 1.531417022 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = 1.531417022 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = 1.531417022 + 1.5 z = 1.531417022 + 1.5 Combine like terms: 1.531417022 + 1.5 = 3.031417022 z = 3.031417022 Simplifying z = 3.031417022

Subproblem 2

z + -1.5 = -1.531417022 Simplifying z + -1.5 = -1.531417022 Reorder the terms: -1.5 + z = -1.531417022 Solving -1.5 + z = -1.531417022 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + z = -1.531417022 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + z = -1.531417022 + 1.5 z = -1.531417022 + 1.5 Combine like terms: -1.531417022 + 1.5 = -0.031417022 z = -0.031417022 Simplifying z = -0.031417022

Solution

The solution to the problem is based on the solutions from the subproblems. z = {3.031417022, -0.031417022}

Solution

z = {3.031417022, -0.031417022}

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