8(3t+4)10t-3+7(2t+5)=

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Solution for 8(3t+4)10t-3+7(2t+5)= equation:


Simplifying
8(3t + 4) * 10t + -3 + 7(2t + 5) = 0

Reorder the terms:
8(4 + 3t) * 10t + -3 + 7(2t + 5) = 0

Reorder the terms for easier multiplication:
8 * 10t(4 + 3t) + -3 + 7(2t + 5) = 0

Multiply 8 * 10
80t(4 + 3t) + -3 + 7(2t + 5) = 0
(4 * 80t + 3t * 80t) + -3 + 7(2t + 5) = 0
(320t + 240t2) + -3 + 7(2t + 5) = 0

Reorder the terms:
320t + 240t2 + -3 + 7(5 + 2t) = 0
320t + 240t2 + -3 + (5 * 7 + 2t * 7) = 0
320t + 240t2 + -3 + (35 + 14t) = 0

Reorder the terms:
-3 + 35 + 320t + 14t + 240t2 = 0

Combine like terms: -3 + 35 = 32
32 + 320t + 14t + 240t2 = 0

Combine like terms: 320t + 14t = 334t
32 + 334t + 240t2 = 0

Solving
32 + 334t + 240t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 167t + 120t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(16 + 167t + 120t2)' equal to zero and attempt to solve: Simplifying 16 + 167t + 120t2 = 0 Solving 16 + 167t + 120t2 = 0 Begin completing the square. Divide all terms by 120 the coefficient of the squared term: Divide each side by '120'. 0.1333333333 + 1.391666667t + t2 = 0.0 Move the constant term to the right: Add '-0.1333333333' to each side of the equation. 0.1333333333 + 1.391666667t + -0.1333333333 + t2 = 0.0 + -0.1333333333 Reorder the terms: 0.1333333333 + -0.1333333333 + 1.391666667t + t2 = 0.0 + -0.1333333333 Combine like terms: 0.1333333333 + -0.1333333333 = 0.0000000000 0.0000000000 + 1.391666667t + t2 = 0.0 + -0.1333333333 1.391666667t + t2 = 0.0 + -0.1333333333 Combine like terms: 0.0 + -0.1333333333 = -0.1333333333 1.391666667t + t2 = -0.1333333333 The t term is 1.391666667t. Take half its coefficient (0.6958333335). Square it (0.4841840280) and add it to both sides. Add '0.4841840280' to each side of the equation. 1.391666667t + 0.4841840280 + t2 = -0.1333333333 + 0.4841840280 Reorder the terms: 0.4841840280 + 1.391666667t + t2 = -0.1333333333 + 0.4841840280 Combine like terms: -0.1333333333 + 0.4841840280 = 0.3508506947 0.4841840280 + 1.391666667t + t2 = 0.3508506947 Factor a perfect square on the left side: (t + 0.6958333335)(t + 0.6958333335) = 0.3508506947 Calculate the square root of the right side: 0.59232651 Break this problem into two subproblems by setting (t + 0.6958333335) equal to 0.59232651 and -0.59232651.

Subproblem 1

t + 0.6958333335 = 0.59232651 Simplifying t + 0.6958333335 = 0.59232651 Reorder the terms: 0.6958333335 + t = 0.59232651 Solving 0.6958333335 + t = 0.59232651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6958333335' to each side of the equation. 0.6958333335 + -0.6958333335 + t = 0.59232651 + -0.6958333335 Combine like terms: 0.6958333335 + -0.6958333335 = 0.0000000000 0.0000000000 + t = 0.59232651 + -0.6958333335 t = 0.59232651 + -0.6958333335 Combine like terms: 0.59232651 + -0.6958333335 = -0.1035068235 t = -0.1035068235 Simplifying t = -0.1035068235

Subproblem 2

t + 0.6958333335 = -0.59232651 Simplifying t + 0.6958333335 = -0.59232651 Reorder the terms: 0.6958333335 + t = -0.59232651 Solving 0.6958333335 + t = -0.59232651 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.6958333335' to each side of the equation. 0.6958333335 + -0.6958333335 + t = -0.59232651 + -0.6958333335 Combine like terms: 0.6958333335 + -0.6958333335 = 0.0000000000 0.0000000000 + t = -0.59232651 + -0.6958333335 t = -0.59232651 + -0.6958333335 Combine like terms: -0.59232651 + -0.6958333335 = -1.2881598435 t = -1.2881598435 Simplifying t = -1.2881598435

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-0.1035068235, -1.2881598435}

Solution

t = {-0.1035068235, -1.2881598435}

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