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Simplifying 6x(x + -1) = (2x + 7)(x + -1) Reorder the terms: 6x(-1 + x) = (2x + 7)(x + -1) (-1 * 6x + x * 6x) = (2x + 7)(x + -1) (-6x + 6x2) = (2x + 7)(x + -1) Reorder the terms: -6x + 6x2 = (7 + 2x)(x + -1) Reorder the terms: -6x + 6x2 = (7 + 2x)(-1 + x) Multiply (7 + 2x) * (-1 + x) -6x + 6x2 = (7(-1 + x) + 2x * (-1 + x)) -6x + 6x2 = ((-1 * 7 + x * 7) + 2x * (-1 + x)) -6x + 6x2 = ((-7 + 7x) + 2x * (-1 + x)) -6x + 6x2 = (-7 + 7x + (-1 * 2x + x * 2x)) -6x + 6x2 = (-7 + 7x + (-2x + 2x2)) Combine like terms: 7x + -2x = 5x -6x + 6x2 = (-7 + 5x + 2x2) Solving -6x + 6x2 = -7 + 5x + 2x2 Solving for variable 'x'. Reorder the terms: 7 + -6x + -5x + 6x2 + -2x2 = -7 + 5x + 2x2 + 7 + -5x + -2x2 Combine like terms: -6x + -5x = -11x 7 + -11x + 6x2 + -2x2 = -7 + 5x + 2x2 + 7 + -5x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 7 + -11x + 4x2 = -7 + 5x + 2x2 + 7 + -5x + -2x2 Reorder the terms: 7 + -11x + 4x2 = -7 + 7 + 5x + -5x + 2x2 + -2x2 Combine like terms: -7 + 7 = 0 7 + -11x + 4x2 = 0 + 5x + -5x + 2x2 + -2x2 7 + -11x + 4x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 7 + -11x + 4x2 = 0 + 2x2 + -2x2 7 + -11x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 7 + -11x + 4x2 = 0 Factor a trinomial. (1 + -1x)(7 + -4x) = 0Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
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 = 1.75Solution
x = {1, 1.75}
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