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Simplifying 6x2 + -7xt + -3t2 = 0 Reorder the terms: -7tx + -3t2 + 6x2 = 0 Solving -7tx + -3t2 + 6x2 = 0 Solving for variable 't'. Factor a trinomial. (-1t + -3x)(3t + -2x) = 0Subproblem 1
Set the factor '(-1t + -3x)' equal to zero and attempt to solve: Simplifying -1t + -3x = 0 Solving -1t + -3x = 0 Move all terms containing t to the left, all other terms to the right. Add '3x' to each side of the equation. -1t + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 -1t + 0 = 0 + 3x -1t = 0 + 3x Remove the zero: -1t = 3x Divide each side by '-1'. t = -3x Simplifying t = -3xSubproblem 2
Set the factor '(3t + -2x)' equal to zero and attempt to solve: Simplifying 3t + -2x = 0 Solving 3t + -2x = 0 Move all terms containing t to the left, all other terms to the right. Add '2x' to each side of the equation. 3t + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 3t + 0 = 0 + 2x 3t = 0 + 2x Remove the zero: 3t = 2x Divide each side by '3'. t = 0.6666666667x Simplifying t = 0.6666666667xSolution
t = {-3x, 0.6666666667x}
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