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Simplifying 6x(x + -3) = (2x + 7)(x + -3) Reorder the terms: 6x(-3 + x) = (2x + 7)(x + -3) (-3 * 6x + x * 6x) = (2x + 7)(x + -3) (-18x + 6x2) = (2x + 7)(x + -3) Reorder the terms: -18x + 6x2 = (7 + 2x)(x + -3) Reorder the terms: -18x + 6x2 = (7 + 2x)(-3 + x) Multiply (7 + 2x) * (-3 + x) -18x + 6x2 = (7(-3 + x) + 2x * (-3 + x)) -18x + 6x2 = ((-3 * 7 + x * 7) + 2x * (-3 + x)) -18x + 6x2 = ((-21 + 7x) + 2x * (-3 + x)) -18x + 6x2 = (-21 + 7x + (-3 * 2x + x * 2x)) -18x + 6x2 = (-21 + 7x + (-6x + 2x2)) Combine like terms: 7x + -6x = 1x -18x + 6x2 = (-21 + 1x + 2x2) Solving -18x + 6x2 = -21 + 1x + 2x2 Solving for variable 'x'. Reorder the terms: 21 + -18x + -1x + 6x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Combine like terms: -18x + -1x = -19x 21 + -19x + 6x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 21 + -19x + 4x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2 Reorder the terms: 21 + -19x + 4x2 = -21 + 21 + 1x + -1x + 2x2 + -2x2 Combine like terms: -21 + 21 = 0 21 + -19x + 4x2 = 0 + 1x + -1x + 2x2 + -2x2 21 + -19x + 4x2 = 1x + -1x + 2x2 + -2x2 Combine like terms: 1x + -1x = 0 21 + -19x + 4x2 = 0 + 2x2 + -2x2 21 + -19x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 21 + -19x + 4x2 = 0 Factor a trinomial. (7 + -4x)(3 + -1x) = 0Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75Subproblem 2
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 = 3Solution
x = {1.75, 3}
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