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Simplifying 6x + -6 + 10 = 5(x + -2)(x + -3) Reorder the terms: -6 + 10 + 6x = 5(x + -2)(x + -3) Combine like terms: -6 + 10 = 4 4 + 6x = 5(x + -2)(x + -3) Reorder the terms: 4 + 6x = 5(-2 + x)(x + -3) Reorder the terms: 4 + 6x = 5(-2 + x)(-3 + x) Multiply (-2 + x) * (-3 + x) 4 + 6x = 5(-2(-3 + x) + x(-3 + x)) 4 + 6x = 5((-3 * -2 + x * -2) + x(-3 + x)) 4 + 6x = 5((6 + -2x) + x(-3 + x)) 4 + 6x = 5(6 + -2x + (-3 * x + x * x)) 4 + 6x = 5(6 + -2x + (-3x + x2)) Combine like terms: -2x + -3x = -5x 4 + 6x = 5(6 + -5x + x2) 4 + 6x = (6 * 5 + -5x * 5 + x2 * 5) 4 + 6x = (30 + -25x + 5x2) Solving 4 + 6x = 30 + -25x + 5x2 Solving for variable 'x'. Reorder the terms: 4 + -30 + 6x + 25x + -5x2 = 30 + -25x + 5x2 + -30 + 25x + -5x2 Combine like terms: 4 + -30 = -26 -26 + 6x + 25x + -5x2 = 30 + -25x + 5x2 + -30 + 25x + -5x2 Combine like terms: 6x + 25x = 31x -26 + 31x + -5x2 = 30 + -25x + 5x2 + -30 + 25x + -5x2 Reorder the terms: -26 + 31x + -5x2 = 30 + -30 + -25x + 25x + 5x2 + -5x2 Combine like terms: 30 + -30 = 0 -26 + 31x + -5x2 = 0 + -25x + 25x + 5x2 + -5x2 -26 + 31x + -5x2 = -25x + 25x + 5x2 + -5x2 Combine like terms: -25x + 25x = 0 -26 + 31x + -5x2 = 0 + 5x2 + -5x2 -26 + 31x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -26 + 31x + -5x2 = 0 Factor a trinomial. (-26 + 5x)(1 + -1x) = 0Subproblem 1
Set the factor '(-26 + 5x)' equal to zero and attempt to solve: Simplifying -26 + 5x = 0 Solving -26 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + 5x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 5x = 0 + 26 5x = 0 + 26 Combine like terms: 0 + 26 = 26 5x = 26 Divide each side by '5'. x = 5.2 Simplifying x = 5.2Subproblem 2
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 = 1Solution
x = {5.2, 1}
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