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Simplifying 6x(3x + 4) = 5x(2x + 8) Reorder the terms: 6x(4 + 3x) = 5x(2x + 8) (4 * 6x + 3x * 6x) = 5x(2x + 8) (24x + 18x2) = 5x(2x + 8) Reorder the terms: 24x + 18x2 = 5x(8 + 2x) 24x + 18x2 = (8 * 5x + 2x * 5x) 24x + 18x2 = (40x + 10x2) Solving 24x + 18x2 = 40x + 10x2 Solving for variable 'x'. Reorder the terms: 24x + -40x + 18x2 + -10x2 = 40x + 10x2 + -40x + -10x2 Combine like terms: 24x + -40x = -16x -16x + 18x2 + -10x2 = 40x + 10x2 + -40x + -10x2 Combine like terms: 18x2 + -10x2 = 8x2 -16x + 8x2 = 40x + 10x2 + -40x + -10x2 Reorder the terms: -16x + 8x2 = 40x + -40x + 10x2 + -10x2 Combine like terms: 40x + -40x = 0 -16x + 8x2 = 0 + 10x2 + -10x2 -16x + 8x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -16x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8x'. 8x(-2 + x) = 0 Ignore the factor 8.Subproblem 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 '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2Solution
x = {0, 2}
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