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Simplifying 45 = (2x + 3)(3x + -4) Reorder the terms: 45 = (3 + 2x)(3x + -4) Reorder the terms: 45 = (3 + 2x)(-4 + 3x) Multiply (3 + 2x) * (-4 + 3x) 45 = (3(-4 + 3x) + 2x * (-4 + 3x)) 45 = ((-4 * 3 + 3x * 3) + 2x * (-4 + 3x)) 45 = ((-12 + 9x) + 2x * (-4 + 3x)) 45 = (-12 + 9x + (-4 * 2x + 3x * 2x)) 45 = (-12 + 9x + (-8x + 6x2)) Combine like terms: 9x + -8x = 1x 45 = (-12 + 1x + 6x2) Solving 45 = -12 + 1x + 6x2 Solving for variable 'x'. Combine like terms: 45 + 12 = 57 57 + -1x + -6x2 = -12 + 1x + 6x2 + 12 + -1x + -6x2 Reorder the terms: 57 + -1x + -6x2 = -12 + 12 + 1x + -1x + 6x2 + -6x2 Combine like terms: -12 + 12 = 0 57 + -1x + -6x2 = 0 + 1x + -1x + 6x2 + -6x2 57 + -1x + -6x2 = 1x + -1x + 6x2 + -6x2 Combine like terms: 1x + -1x = 0 57 + -1x + -6x2 = 0 + 6x2 + -6x2 57 + -1x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 57 + -1x + -6x2 = 0 Factor a trinomial. (3 + -1x)(19 + 6x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 2
Set the factor '(19 + 6x)' equal to zero and attempt to solve: Simplifying 19 + 6x = 0 Solving 19 + 6x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + 6x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 6x = 0 + -19 6x = 0 + -19 Combine like terms: 0 + -19 = -19 6x = -19 Divide each side by '6'. x = -3.166666667 Simplifying x = -3.166666667Solution
x = {3, -3.166666667}
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