2(3h-1)4h=10(2-3h)+38h

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Solution for 2(3h-1)4h=10(2-3h)+38h equation:


Simplifying
2(3h + -1) * 4h = 10(2 + -3h) + 38h

Reorder the terms:
2(-1 + 3h) * 4h = 10(2 + -3h) + 38h

Reorder the terms for easier multiplication:
2 * 4h(-1 + 3h) = 10(2 + -3h) + 38h

Multiply 2 * 4
8h(-1 + 3h) = 10(2 + -3h) + 38h
(-1 * 8h + 3h * 8h) = 10(2 + -3h) + 38h
(-8h + 24h2) = 10(2 + -3h) + 38h
-8h + 24h2 = (2 * 10 + -3h * 10) + 38h
-8h + 24h2 = (20 + -30h) + 38h

Combine like terms: -30h + 38h = 8h
-8h + 24h2 = 20 + 8h

Solving
-8h + 24h2 = 20 + 8h

Solving for variable 'h'.

Reorder the terms:
-20 + -8h + -8h + 24h2 = 20 + 8h + -20 + -8h

Combine like terms: -8h + -8h = -16h
-20 + -16h + 24h2 = 20 + 8h + -20 + -8h

Reorder the terms:
-20 + -16h + 24h2 = 20 + -20 + 8h + -8h

Combine like terms: 20 + -20 = 0
-20 + -16h + 24h2 = 0 + 8h + -8h
-20 + -16h + 24h2 = 8h + -8h

Combine like terms: 8h + -8h = 0
-20 + -16h + 24h2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + -4h + 6h2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-5 + -4h + 6h2)' equal to zero and attempt to solve: Simplifying -5 + -4h + 6h2 = 0 Solving -5 + -4h + 6h2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -0.6666666667h + h2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -0.6666666667h + 0.8333333333 + h2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -0.6666666667h + h2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -0.6666666667h + h2 = 0 + 0.8333333333 -0.6666666667h + h2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -0.6666666667h + h2 = 0.8333333333 The h term is -0.6666666667h. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667h + 0.1111111112 + h2 = 0.8333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667h + h2 = 0.8333333333 + 0.1111111112 Combine like terms: 0.8333333333 + 0.1111111112 = 0.9444444445 0.1111111112 + -0.6666666667h + h2 = 0.9444444445 Factor a perfect square on the left side: (h + -0.3333333334)(h + -0.3333333334) = 0.9444444445 Calculate the square root of the right side: 0.971825316 Break this problem into two subproblems by setting (h + -0.3333333334) equal to 0.971825316 and -0.971825316.

Subproblem 1

h + -0.3333333334 = 0.971825316 Simplifying h + -0.3333333334 = 0.971825316 Reorder the terms: -0.3333333334 + h = 0.971825316 Solving -0.3333333334 + h = 0.971825316 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + h = 0.971825316 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + h = 0.971825316 + 0.3333333334 h = 0.971825316 + 0.3333333334 Combine like terms: 0.971825316 + 0.3333333334 = 1.3051586494 h = 1.3051586494 Simplifying h = 1.3051586494

Subproblem 2

h + -0.3333333334 = -0.971825316 Simplifying h + -0.3333333334 = -0.971825316 Reorder the terms: -0.3333333334 + h = -0.971825316 Solving -0.3333333334 + h = -0.971825316 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.3333333334' to each side of the equation. -0.3333333334 + 0.3333333334 + h = -0.971825316 + 0.3333333334 Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000 0.0000000000 + h = -0.971825316 + 0.3333333334 h = -0.971825316 + 0.3333333334 Combine like terms: -0.971825316 + 0.3333333334 = -0.6384919826 h = -0.6384919826 Simplifying h = -0.6384919826

Solution

The solution to the problem is based on the solutions from the subproblems. h = {1.3051586494, -0.6384919826}

Solution

h = {1.3051586494, -0.6384919826}

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