-2(t+6)=5t(t+1)

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Solution for -2(t+6)=5t(t+1) equation:


Simplifying
-2(t + 6) = 5t(t + 1)

Reorder the terms:
-2(6 + t) = 5t(t + 1)
(6 * -2 + t * -2) = 5t(t + 1)
(-12 + -2t) = 5t(t + 1)

Reorder the terms:
-12 + -2t = 5t(1 + t)
-12 + -2t = (1 * 5t + t * 5t)
-12 + -2t = (5t + 5t2)

Solving
-12 + -2t = 5t + 5t2

Solving for variable 't'.

Combine like terms: -2t + -5t = -7t
-12 + -7t + -5t2 = 5t + 5t2 + -5t + -5t2

Reorder the terms:
-12 + -7t + -5t2 = 5t + -5t + 5t2 + -5t2

Combine like terms: 5t + -5t = 0
-12 + -7t + -5t2 = 0 + 5t2 + -5t2
-12 + -7t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
-12 + -7t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 7t + 5t2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(12 + 7t + 5t2)' equal to zero and attempt to solve: Simplifying 12 + 7t + 5t2 = 0 Solving 12 + 7t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 1.4t + t2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 1.4t + -2.4 + t2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 1.4t + t2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 1.4t + t2 = 0 + -2.4 1.4t + t2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 1.4t + t2 = -2.4 The t term is 1.4t. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4t + 0.49 + t2 = -2.4 + 0.49 Reorder the terms: 0.49 + 1.4t + t2 = -2.4 + 0.49 Combine like terms: -2.4 + 0.49 = -1.91 0.49 + 1.4t + t2 = -1.91 Factor a perfect square on the left side: (t + 0.7)(t + 0.7) = -1.91 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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