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Simplifying (2x + -5)(3x + -4) = (5x + 4)(x + 5) Reorder the terms: (-5 + 2x)(3x + -4) = (5x + 4)(x + 5) Reorder the terms: (-5 + 2x)(-4 + 3x) = (5x + 4)(x + 5) Multiply (-5 + 2x) * (-4 + 3x) (-5(-4 + 3x) + 2x * (-4 + 3x)) = (5x + 4)(x + 5) ((-4 * -5 + 3x * -5) + 2x * (-4 + 3x)) = (5x + 4)(x + 5) ((20 + -15x) + 2x * (-4 + 3x)) = (5x + 4)(x + 5) (20 + -15x + (-4 * 2x + 3x * 2x)) = (5x + 4)(x + 5) (20 + -15x + (-8x + 6x2)) = (5x + 4)(x + 5) Combine like terms: -15x + -8x = -23x (20 + -23x + 6x2) = (5x + 4)(x + 5) Reorder the terms: 20 + -23x + 6x2 = (4 + 5x)(x + 5) Reorder the terms: 20 + -23x + 6x2 = (4 + 5x)(5 + x) Multiply (4 + 5x) * (5 + x) 20 + -23x + 6x2 = (4(5 + x) + 5x * (5 + x)) 20 + -23x + 6x2 = ((5 * 4 + x * 4) + 5x * (5 + x)) 20 + -23x + 6x2 = ((20 + 4x) + 5x * (5 + x)) 20 + -23x + 6x2 = (20 + 4x + (5 * 5x + x * 5x)) 20 + -23x + 6x2 = (20 + 4x + (25x + 5x2)) Combine like terms: 4x + 25x = 29x 20 + -23x + 6x2 = (20 + 29x + 5x2) Add '-20' to each side of the equation. 20 + -23x + -20 + 6x2 = 20 + 29x + -20 + 5x2 Reorder the terms: 20 + -20 + -23x + 6x2 = 20 + 29x + -20 + 5x2 Combine like terms: 20 + -20 = 0 0 + -23x + 6x2 = 20 + 29x + -20 + 5x2 -23x + 6x2 = 20 + 29x + -20 + 5x2 Reorder the terms: -23x + 6x2 = 20 + -20 + 29x + 5x2 Combine like terms: 20 + -20 = 0 -23x + 6x2 = 0 + 29x + 5x2 -23x + 6x2 = 29x + 5x2 Solving -23x + 6x2 = 29x + 5x2 Solving for variable 'x'. Reorder the terms: -23x + -29x + 6x2 + -5x2 = 29x + 5x2 + -29x + -5x2 Combine like terms: -23x + -29x = -52x -52x + 6x2 + -5x2 = 29x + 5x2 + -29x + -5x2 Combine like terms: 6x2 + -5x2 = 1x2 -52x + 1x2 = 29x + 5x2 + -29x + -5x2 Reorder the terms: -52x + 1x2 = 29x + -29x + 5x2 + -5x2 Combine like terms: 29x + -29x = 0 -52x + 1x2 = 0 + 5x2 + -5x2 -52x + 1x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -52x + 1x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-52 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-52 + x)' equal to zero and attempt to solve: Simplifying -52 + x = 0 Solving -52 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + x = 0 + 52 Combine like terms: -52 + 52 = 0 0 + x = 0 + 52 x = 0 + 52 Combine like terms: 0 + 52 = 52 x = 52 Simplifying x = 52Solution
x = {0, 52}
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