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Simplifying 4(x + -3) + -1r + 2x = 5(3x + -7) * 9x Reorder the terms: 4(-3 + x) + -1r + 2x = 5(3x + -7) * 9x (-3 * 4 + x * 4) + -1r + 2x = 5(3x + -7) * 9x (-12 + 4x) + -1r + 2x = 5(3x + -7) * 9x Reorder the terms: -12 + -1r + 4x + 2x = 5(3x + -7) * 9x Combine like terms: 4x + 2x = 6x -12 + -1r + 6x = 5(3x + -7) * 9x Reorder the terms: -12 + -1r + 6x = 5(-7 + 3x) * 9x Reorder the terms for easier multiplication: -12 + -1r + 6x = 5 * 9x(-7 + 3x) Multiply 5 * 9 -12 + -1r + 6x = 45x(-7 + 3x) -12 + -1r + 6x = (-7 * 45x + 3x * 45x) -12 + -1r + 6x = (-315x + 135x2) Solving -12 + -1r + 6x = -315x + 135x2 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '12' to each side of the equation. -12 + -1r + 12 + 6x = -315x + 12 + 135x2 Reorder the terms: -12 + 12 + -1r + 6x = -315x + 12 + 135x2 Combine like terms: -12 + 12 = 0 0 + -1r + 6x = -315x + 12 + 135x2 -1r + 6x = -315x + 12 + 135x2 Reorder the terms: -1r + 6x = 12 + -315x + 135x2 Add '-6x' to each side of the equation. -1r + 6x + -6x = 12 + -315x + -6x + 135x2 Combine like terms: 6x + -6x = 0 -1r + 0 = 12 + -315x + -6x + 135x2 -1r = 12 + -315x + -6x + 135x2 Combine like terms: -315x + -6x = -321x -1r = 12 + -321x + 135x2 Divide each side by '-1'. r = -12 + 321x + -135x2 Simplifying r = -12 + 321x + -135x2
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