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Simplifying 4x2 + 15 = 2x2 + 3(7x + 5) Reorder the terms: 15 + 4x2 = 2x2 + 3(7x + 5) Reorder the terms: 15 + 4x2 = 2x2 + 3(5 + 7x) 15 + 4x2 = 2x2 + (5 * 3 + 7x * 3) 15 + 4x2 = 2x2 + (15 + 21x) Reorder the terms: 15 + 4x2 = 15 + 21x + 2x2 Add '-15' to each side of the equation. 15 + -15 + 4x2 = 15 + 21x + -15 + 2x2 Combine like terms: 15 + -15 = 0 0 + 4x2 = 15 + 21x + -15 + 2x2 4x2 = 15 + 21x + -15 + 2x2 Reorder the terms: 4x2 = 15 + -15 + 21x + 2x2 Combine like terms: 15 + -15 = 0 4x2 = 0 + 21x + 2x2 4x2 = 21x + 2x2 Solving 4x2 = 21x + 2x2 Solving for variable 'x'. Reorder the terms: -21x + 4x2 + -2x2 = 21x + 2x2 + -21x + -2x2 Combine like terms: 4x2 + -2x2 = 2x2 -21x + 2x2 = 21x + 2x2 + -21x + -2x2 Reorder the terms: -21x + 2x2 = 21x + -21x + 2x2 + -2x2 Combine like terms: 21x + -21x = 0 -21x + 2x2 = 0 + 2x2 + -2x2 -21x + 2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -21x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-21 + 2x) = 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 '(-21 + 2x)' equal to zero and attempt to solve: Simplifying -21 + 2x = 0 Solving -21 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + 2x = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 2x = 0 + 21 2x = 0 + 21 Combine like terms: 0 + 21 = 21 2x = 21 Divide each side by '2'. x = 10.5 Simplifying x = 10.5Solution
x = {0, 10.5}
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