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Simplifying 6x(x + -6) = (2x + 5)(x + -6) Reorder the terms: 6x(-6 + x) = (2x + 5)(x + -6) (-6 * 6x + x * 6x) = (2x + 5)(x + -6) (-36x + 6x2) = (2x + 5)(x + -6) Reorder the terms: -36x + 6x2 = (5 + 2x)(x + -6) Reorder the terms: -36x + 6x2 = (5 + 2x)(-6 + x) Multiply (5 + 2x) * (-6 + x) -36x + 6x2 = (5(-6 + x) + 2x * (-6 + x)) -36x + 6x2 = ((-6 * 5 + x * 5) + 2x * (-6 + x)) -36x + 6x2 = ((-30 + 5x) + 2x * (-6 + x)) -36x + 6x2 = (-30 + 5x + (-6 * 2x + x * 2x)) -36x + 6x2 = (-30 + 5x + (-12x + 2x2)) Combine like terms: 5x + -12x = -7x -36x + 6x2 = (-30 + -7x + 2x2) Solving -36x + 6x2 = -30 + -7x + 2x2 Solving for variable 'x'. Reorder the terms: 30 + -36x + 7x + 6x2 + -2x2 = -30 + -7x + 2x2 + 30 + 7x + -2x2 Combine like terms: -36x + 7x = -29x 30 + -29x + 6x2 + -2x2 = -30 + -7x + 2x2 + 30 + 7x + -2x2 Combine like terms: 6x2 + -2x2 = 4x2 30 + -29x + 4x2 = -30 + -7x + 2x2 + 30 + 7x + -2x2 Reorder the terms: 30 + -29x + 4x2 = -30 + 30 + -7x + 7x + 2x2 + -2x2 Combine like terms: -30 + 30 = 0 30 + -29x + 4x2 = 0 + -7x + 7x + 2x2 + -2x2 30 + -29x + 4x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 30 + -29x + 4x2 = 0 + 2x2 + -2x2 30 + -29x + 4x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + -29x + 4x2 = 0 Factor a trinomial. (5 + -4x)(6 + -1x) = 0Subproblem 1
Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {1.25, 6}
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