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Simplifying (6x + -5)(x + -3) = (4x + 1)(x + -3) Reorder the terms: (-5 + 6x)(x + -3) = (4x + 1)(x + -3) Reorder the terms: (-5 + 6x)(-3 + x) = (4x + 1)(x + -3) Multiply (-5 + 6x) * (-3 + x) (-5(-3 + x) + 6x * (-3 + x)) = (4x + 1)(x + -3) ((-3 * -5 + x * -5) + 6x * (-3 + x)) = (4x + 1)(x + -3) ((15 + -5x) + 6x * (-3 + x)) = (4x + 1)(x + -3) (15 + -5x + (-3 * 6x + x * 6x)) = (4x + 1)(x + -3) (15 + -5x + (-18x + 6x2)) = (4x + 1)(x + -3) Combine like terms: -5x + -18x = -23x (15 + -23x + 6x2) = (4x + 1)(x + -3) Reorder the terms: 15 + -23x + 6x2 = (1 + 4x)(x + -3) Reorder the terms: 15 + -23x + 6x2 = (1 + 4x)(-3 + x) Multiply (1 + 4x) * (-3 + x) 15 + -23x + 6x2 = (1(-3 + x) + 4x * (-3 + x)) 15 + -23x + 6x2 = ((-3 * 1 + x * 1) + 4x * (-3 + x)) 15 + -23x + 6x2 = ((-3 + 1x) + 4x * (-3 + x)) 15 + -23x + 6x2 = (-3 + 1x + (-3 * 4x + x * 4x)) 15 + -23x + 6x2 = (-3 + 1x + (-12x + 4x2)) Combine like terms: 1x + -12x = -11x 15 + -23x + 6x2 = (-3 + -11x + 4x2) Solving 15 + -23x + 6x2 = -3 + -11x + 4x2 Solving for variable 'x'. Reorder the terms: 15 + 3 + -23x + 11x + 6x2 + -4x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2 Combine like terms: 15 + 3 = 18 18 + -23x + 11x + 6x2 + -4x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2 Combine like terms: -23x + 11x = -12x 18 + -12x + 6x2 + -4x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2 Combine like terms: 6x2 + -4x2 = 2x2 18 + -12x + 2x2 = -3 + -11x + 4x2 + 3 + 11x + -4x2 Reorder the terms: 18 + -12x + 2x2 = -3 + 3 + -11x + 11x + 4x2 + -4x2 Combine like terms: -3 + 3 = 0 18 + -12x + 2x2 = 0 + -11x + 11x + 4x2 + -4x2 18 + -12x + 2x2 = -11x + 11x + 4x2 + -4x2 Combine like terms: -11x + 11x = 0 18 + -12x + 2x2 = 0 + 4x2 + -4x2 18 + -12x + 2x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 18 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -6x + x2) = 0 Factor a trinomial. 2((3 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 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 '(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 = {3, 3}
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