(3t-4)(3t-4)-7(3t-4)+10=0

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Solution for (3t-4)(3t-4)-7(3t-4)+10=0 equation:


Simplifying
(3t + -4)(3t + -4) + -7(3t + -4) + 10 = 0

Reorder the terms:
(-4 + 3t)(3t + -4) + -7(3t + -4) + 10 = 0

Reorder the terms:
(-4 + 3t)(-4 + 3t) + -7(3t + -4) + 10 = 0

Multiply (-4 + 3t) * (-4 + 3t)
(-4(-4 + 3t) + 3t * (-4 + 3t)) + -7(3t + -4) + 10 = 0
((-4 * -4 + 3t * -4) + 3t * (-4 + 3t)) + -7(3t + -4) + 10 = 0
((16 + -12t) + 3t * (-4 + 3t)) + -7(3t + -4) + 10 = 0
(16 + -12t + (-4 * 3t + 3t * 3t)) + -7(3t + -4) + 10 = 0
(16 + -12t + (-12t + 9t2)) + -7(3t + -4) + 10 = 0

Combine like terms: -12t + -12t = -24t
(16 + -24t + 9t2) + -7(3t + -4) + 10 = 0

Reorder the terms:
16 + -24t + 9t2 + -7(-4 + 3t) + 10 = 0
16 + -24t + 9t2 + (-4 * -7 + 3t * -7) + 10 = 0
16 + -24t + 9t2 + (28 + -21t) + 10 = 0

Reorder the terms:
16 + 28 + 10 + -24t + -21t + 9t2 = 0

Combine like terms: 16 + 28 = 44
44 + 10 + -24t + -21t + 9t2 = 0

Combine like terms: 44 + 10 = 54
54 + -24t + -21t + 9t2 = 0

Combine like terms: -24t + -21t = -45t
54 + -45t + 9t2 = 0

Solving
54 + -45t + 9t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '9'.
9(6 + -5t + t2) = 0

Factor a trinomial.
9((2 + -1t)(3 + -1t)) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2

Subproblem 2

Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3

Solution

t = {2, 3}

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